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MIL-HDBK-781
14 July 1987
Ml LITARY
Reliability Test
HANDBOOK
Methods, Plans,
and Environments for
Engineering Development,
Qualification, and Production
No deliverable data required by thk document.
AREA RELI
DISTRIBUTION STATEMENT A:Approved for public release: distribution is unlimited.
MIL-HDBK-781
Department OF DEFENSEWashington. Or 20363 .s100
Reliability Tesl Methods Plan% And Environments For Engineering
Oevelopmenl, Qualification, And Production
I Thi$ Military Handbook is approved for use by all Departments and Agencie$ of the DeparImenl of
Oefen$e
2. Beneficial commen!s [recommendations. addmom, deletions) and any perlinenl data which may
be of use in improving thi$ document should be addressed 10: Commander, Space and Naval WarfareSptem$ Command, AlTN: SPAWAR 003-121. Wa$hmglon, DC 20363-5100. by u~ing the self -addressedStandardization Document Improvement Propmal (OD Form 1426) appearing al the ●nd of lhIS document orby letter
0
t!
1!
L . . . ..___-_._../_.
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MIL-HDBK-781
FOREWORD
1. MIL. HDBK.7B1 ii designed to be u$ed with MIL.STD-781. The test methods, te!l plan!, andenvironmental profile data are presented ,n a manner which facilitates their use with the ta,lor able ta~k$ ofMI L-STD.781.
2. The testing of electronic equipment procured for new military $yslem$ is an increasingly complexprocess Reliability engineers and ma~er$ must select test methods. test plans, and t.?$t ●nv!ronmenl$which will enwre that cont,accually required reliability Ievel$ are attained in the field and early defectfailures are removed prtor to field deployment MIL-HD8K-781 provides reliability ●ngineers and managerswith a menu of test plans, test methods, and environmental profiles. The mo$t appropriate material maybeselected for each program and incorporated into lhe tailored reliability test program derived fromMIL-STD-781.
3. This handbook IS wr, tten for use by the reliability engineer and manager. The sections onrel, abil, ty Ie$t methods and lest plan$ presenl melhods for growth monitoring. environmental stress
screen, ng, mean. ume. between. failufe a$wrance testing, sequential tests. fixed-durat!on Ies:s, and all-
equtpmen! tests The wctmns on Ies! enwronmemal profiles provide test environments for f,xed-grou~dequ, pment. momte ground vehicle, shipboard. jet aircraft, turboprop and helicopter. and m,ss,les and
assembled ealerna! stores eau, pment The references provided will expand the u$er’> knowledge and ?mdInthe destgn and implementation of re)!ab!l,ly Ie%l programs through more delailed data
Ill
CONTENTS
I
Paragraph
1
111.21,2 I1.2 :
1.31.4
2
2. i2.1 “.2., :
33. a.,:;
3:?3.!3
3.1.4
3.1.53.1.6
3.1.7
3.1.83.1.9
4.4.14.!.14.1.2
4.1.34.1,44.2
&2. i4.2.24.34.3.14.3,24.4
4.4. !
4.4.24.4.34.5
4.5.1
4.s.24.5
SCOPE .,,
Purpose . . . . . . . . . . . . . . . . .
Applicability . . . . . . .Application of handbook.Taiioring.h~e;h,cdci!refe:eeoce
Equipmentcategori=
REFERENCE DOCUMENTS
Government documents . . . . . . . .specificaliGns, Siafidard$, and %m%ak.$Olher Government documents
DEFINITIONS . . . . . . . . .Term% . . . . . . . . .
Contractor . . . . . . . .Corrective maintenance (repair)Decision risk~Failures . . . . . . . . .Independent chargeable failure categories
Measures oirei!abiiity . . . . . .
Mis$ion profile . . . . . . . . . . . . . .Life-cycle profile
Procuring activity . . . . . .
RELIABILITY TEST METIIODSANDTEST P@NSPurpos e . . . . . . . . . . . . . . . .c.. ---p . . . . . .Applicatiomm atria.... . . . . . . . .Te%t methods . . . . . . . . . . . . . . .
Te\t plans . . . . . . . . . . . . . . . . . .Test method and test plan selection factors
Test melhti and test pliir, $ekder,
Tes! method and%! plan pararnew$ebc!icmReliability DevelopmenVGrowth Evaluation Methods
The Duane Method . . . . . . . . . . . . . . . . .The AMSAAMethod . . . . . . . . . . . . . . . . . .E.SmOnilOringm etho6s
Ccmpti:ed CA time irotewa! m.et%dGraphical me!h~
Standard EMS . . . . . . . . .;;;;;;.~;MTBFaswrance test....
Derivation of equation.Procedure . . . . . . . .
Sequen:ia! :enp!an: . . . . . . .
iv
Page
1
111
i
11
4Q~
44A
4
5s
5
5
66666
6667
8811;5Is
16161718
1919
Paragraph
cONTENTS(Continued)
Page
.
.
4.6.14.6.2
4.6.34.6.44.6.54.6.6
4.6.74.6.8
4.74.7.14.7.24.7.3
4,7.44.7.54.7.64.7.747.8
4.7.94.7.10A8
4.8.14.8.2
4.8.34.84
4.94.9,14.9.2
4.9.34.9.44.9.54.9.64.9.74.9.8
5.s 1
5.1.15.2
5.2.15.2.25.3
5.315.3.2
5.3.3
Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . j:Application . . . . . . . . . . . . . . . . . . . . .Theoretical background 21
Test truncation . . . . . . . . . . . . . . . . . . . . . . . .?3
Sequential testexamP1e 23
Standard PRST accepl-rejecl criteria and OC curves 2s
Confidence limits for sequential test$ . 25
Sequential tetts: Program Manager’$ as$e$$ment. . 2-I
Fjxed-duralion leS1s . . . . . . . . . . . . . . . . . . 28
Symbols . . . . . . . . . . . . . . . . . . . . . . . . 28
Example problem . . . . . . . . . . . . . . . . . . . . . 29
Standard fixed.durat,on test plans and OC curves 29
Alternative fixed-duration te$t plans 30
MTBF est, mat, on from observed lest data 30
Exclusion of hypothesm lesivalue$ 30
Specified con f,denceinlerval 30
MTBF est$matton from f,xed-duralion test plans 30
Projecuonof erper,ed field MTBF 32
Fixed-duration tesls. Program Manager’s a%%es%ment 32
All-equipment Production Reliability Acceptance Test Plan 33
Tesldurauon . . . . . . . . . . . . . . . . . . 33
Evaluation . . . . . . . . . . . . . . . . . . . . . . 33
Accepl. re)ect criteria for the ail-equipment IeSl 33
Add, uonal al!-equ, pmenl production reliability
acceptance lest plans.. . . . . . . . . . . . . 34
Reloabll,ty estimate% from unit.level results 34
Calculawmm ethos . . . . . . . . . . . . . . . . . . . . 34
Numertical esample$ . . . . . . . . . . . . . . . . 36
The ca%eolonlyone failure Insomesubsyslem(s) 38
An estimator of the failure rate upper bound AO
Depaflure$ from AO method requirements 40
Noobsecved failures . . . . . . . . . . . . . . . . 41
Typelcemoring . . . . . . . . . . . . . . . . 42
Compmerp rogram . . . . . . . . . . . . . . . . 42
COMBINEO ENVIRONMENTAL TEST CONDITIONS 44
Purpose . . . . . . . . . . . . . . . . . . . . . . . . 44
Scope . . . . . . . . . . . . . . . . . . . . . . . 44
M#ss,on and Ii fe.cycle en.lronmental PrOfile$ and ~e~tconditions . . . . . . . . . . . . . . . . . . . A4
Mission and life-cycle environmental Profiles 44
Environmental testcond,tlons. 44
Combined environments for fixed-ground equipmenl 44
Electrmwc stress and duly cycle 44
Vbbralion stress . . . . . . . . . . . . . . . . . . . . . 45
Thermal stress . . . . . . . . . . . . . . . . . . . . . 45
v
CONTENTS (ContinueO)
Paragrapt,
5.3.4
5.45.4.15.4.2
5.4.35.4.45.5
551
5.5.25.535.54
5656!56.25.635.6.456.5
5.7
5.7.15.7.2
5.7.35.7.4
57.55.7.65.7.7
5.8
5.8.1S.8 2
5.9
S.9 1S.9.2
5.9.3S.lo5.10.1
6.
6.16.1.16.2
6.2.1
6226.2.3
Hum, d,ty
Combbned environments for mobile ground equipment
Electrical $IressanddutycycleVibration Stre$s
Thermal stress . .
Moisture .
Combined environment% for shipboard and underwatervehicle equipment$
Naval surface crall .,.
Naval wbmanneMar$ne crab (Army) .,. .
Underwalervehicle$Combined environments for [et aircraft equipmentMission profilesEnv, ronmemal test profde~Comtrucbon of anenv,ronmenlal profileTest proftle development .,.
COmpOslle enwronmental Iesl profile formultlm, sslonappl, cattons
Comb, ned environments f,>, VfiTOL equtpmeniM,s%ion de$cr, pl, on
Thermal \tress
V, bralion $IressElectr!ca~ %uessHum!d81~
Equipment operationTest pro fnle~
Comb, ned environments for wrbopropeller atrcratl andhel, coplerequipmenl . . . . . . . . . . . . . . .Turbopropeller alrcrah environments
Heljcopler environments
Comb,ned environments for a,r-launched weaponsand a$!embled external storesM,won’proftle%, . . . . . . . . . . . . . . . . . .
Environmental lest profile%
Example of construction of environmental profileW$sile transponauon, handl!ng, and storageRail transpon condluom . . . .
TEST INSTRUMENTATION AND FACILITIES.Purp05e . . . . . . . . . . . . . . . . . . . . . . . .
Scope . . . . . . . . . . . . . . . . . . . . . . . . . .Te$I Iacilltie$and apparatus.
Te$l chambers, . . . . . . . . . . . . . . . . .
Equipment cooling . . . . . .Test in%trumenlat!on .
Page
4s4s
4s46
4646
46464849
so50so50S&S4
5558S9
59
595960
6060
6060
61
61
6162
666767
69
6969
69696970
VI
I
6,2.4
6.2.56.2.6
6.2.7
7.
TABLE
1
2
345
67
89A
96
10A
108
1112
13
1415
16
17
lB
19
20
21
22
MIL-HDBK-781
CONTENTS IContinuedl
Cdibrmiona nd. ccumcv. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Tes!ing the:est focilky . . . . . . . . . . . . . . . . . . . . . . . . . . .Installation oftietest tiamintk test facilii . . . . . . . . . . . . . . . . . . . . .
Sub;ect WJm{Keywordlfk iW... . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
TA6LES
Apdicntion mmri x . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Summarv olvariables forthe AMSAA model . . . . . . . . . . . . . . . . . . . . . . .
Summarv ofeauations, AMSAA model . . . . . . . .Equalion 6election guide, AMSAA model . . . . . . . . .Critical va!ues of C: mvamettic form of the
Cramm.Von M,sesstatintic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Confidence intervals for MTOF. Iailure.terminmed test
Confidence intervals for MTBF, time.terminated tesl . . . . . . . .AMSAAmodel eaamole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
( 1 .>1 100 oercem standard confidence limits on MTBF atiet
Bccenldecision llowet. OL”l>.i)l . . . . . . . . . . . . . . . . . . . . . . . .
(1 II 100 oe.rcent acertdare Canf idence limits on MTBF aher,,accepldec,s#on luvper.0u17,all . . . . . . . . . . . . . . . . . . . . . .
(1 .>1 1Od percent standard Conf idnnce limits on MTBF afterreiectdecicion llowe, -R,”l>.1)) . . . . . . . . . . . . . . . . . . . . . .
11 .,1 100 percent mnndard confidence Iimim on MTeF after
rejec!decision (upper .O~lv.111 . . . . . . . . . . . . . . . . . . . . . . . . . .Summarv oftixed4wntion te.l plans. . . . . . . . . . . . . . . . . . . . . . . . . . . .Summary of high risk freed-duration test plans . . . . . . . . . . . . . . . . .Demonstrnled MTBF confidence limit multipliers. for failure calculatmn
Dnmonstcnted MT9F confidence limit mu ftipliefs, for time cnlculalionAccept times of fixedduralion test plans, Proeram Manager’s
Assessment !.... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Compari80n of risks. standard fixed. duration tests versus PrOQ,BmMamwer’sAs sessmant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Test times, .Wmdafd fixad-dumtion tes! plans versus ProgramManaQer.a Assessmanl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Failure times fofthe numerical example . . . . . . . . . . . . . . . . . . . . . . . . . .
Example of correct ordering in the AO bound calculation . . . .
Example of incorrect ordering in the AO bound calculation
Example data for computer program. . . . . . . . . . . . . . . . . . . . . . . . . . . . .Exnmple computer run fordatain TA8LE 21 . . . . . . . . . . . . . . . . . . . . . . .
vii
I—.
7070
70
70
71
Page
73
74
75
76
7778
79
80
81
66
90
95100
100101102
103
106
107106
109110
111112
—..——
MIL-HDBK-7B1
CONTENTS (Continued)
I TASLE Page
2324
I 25
26
27
I 29
30
31323334
353637
E404142
4344
454647
4.9
49
so
515253
54
Thermal stress environments for marine crabEnvironmental profile data (example)
Test profile data (example)HOI day temperatures ~C) for Cla$s I equipment in air-
conditioned compartmentsHOI day ambient temperature (“C) for Class II equipmentinair<ond, tioned companmentsHot day ambient temperatures ~C) for ●quipment in ram
air-cooled companmemsCold day arnb, enl temperatures ~C) for equipment ir?
ram air-cooled compartmentsTemperatures ~C) for Clasi I and Class II equipmenl,n air-conditioned companments
Jet aircrafi random vibration lest.Tabulation of temperature valuesSummary of temperature valuesTabula; ,onof wbrallon Ievel$
Summary of vi brat$on levelsComposite test prof,le t,mel, neTemperature level Iab”lat, on hot day(example)Temperature summary - hot day (example)Temperature level labulation - cold day (e,ample)
Temperature summary cold day (example)V, bral,on level Iabulal,on (e,ample)V, bral, on level wmmary (example)Temperaw,e rate of change (example)
Composite test prof,le timeli,>e (example)Random vibration test for Vf5TOLaircratlEnv8r0nmenlal pro f,lesequence
Stores hosl a,rcrati m,ssion utlllzat, on ratei forenwronmental testing
Random wbratmn. 9,-, [OVL), level adluslmenl fanorsfor the max, mum predicted environment (951h percentilewith 50 percent confidence based on one+ide tolerancelimO1)
113
114115
116
116
lt7
117
118119
120120121121
122123123124
124125125
126
127128129
130
131Method of calculating the acceleration power spectral den!ily
u
spectrum to produce ~ A, ●qual 10a unit - g,m, (OVL) 132
,.1Preliminary operational des,gn requirements (expected
lifeof5years) . . . . . . . . . 135
Life cycle environments 140
Assumed typ!cal a!tack mission profiles 158
A method for calculating test profde ttmes for a
specific number of test cycles 159
Attack a!rcran caplive-carriage mission profole
data (e~ample) 161
VIII
.
,
TAELE
2324
2526
27
28
29
30
313233
343536
3738394041
42
4344454647
4a
49
so
S152
53
54
cONTENTS (Continued)
Thermal stress environments for marine crafl
Environmental profile data (example)Ten orofile data (example)
. .
Hot day temperatures rC) for Class I equipment in air-conditioned companmentsHot day ambient temperature ~C) for Clas\ II equipmentin air-conditioned compaflments
Hot day ambient temperatures CC) for equipment in ramair-cooled companmentsCold day ambient temperatures ~C) for equipment inram air-cooled companmenls
Temperature ~C) for Class I and Clasi II equipmentin air-conditioned companment$Jet aircrafi random vi brationte$l.Tabulation of temperature values
5ummary0f lemperaturevaluesTabulat# on of vi bratl on levels
Summary of vibration le.elsComposite test pro file ttmehneTemperature ievel tabulal,on hotday(example)
Temperature summary - hot day (example)Temperature level tabulation - cold day (example)Temperature summary. co!d day(e~ample)Vlbralion level tabulatmn (example)
Vibralion level summary (example)Temperature rale of change (example).
Composite :est prof,le timeliew (example)Random viblation tesl for V/5TOL aircratl.
Enwronmenlal profnle sequenceStores host a,rcraft m,ssion utilization rate% for
environmental testingRandom wbration, g,-, (OVL). level adjustment factorsfor the max!mum predicted environment (95th percentile
with SO percent confidence based on one-side tolerancelimit) . . . . .
Mel hod of calculati ng the acceleration power spenral den!ity
spectrum to produce ~+ equaltOauni~-g,m,(OvL)
Preliminary operational design requirements (expected
life0f5years) . . . . . . . . . . . . . . . . . . . . . . .Lifecycle environmentsAssumed typical attack mimion profilesA method for Calculal, ng test profile times for a
specific number of test cyclesAttack aircrafl captive-carriage mission profile
data (example) . . . . . . . . . . . . . . . . . . . .
Page
113
114115
116
116
117
117
118119120
120121
121
122123
123124124
125125
126127128
129
130
131
132
135140158
159
161
Vlll
MIL-HDBK-781
CONTENTS (Continued)
FIGuRE
27
2829
303132
33343s36
37383940414243
444541!
51
52
53
5455
56
s?
58
59
60
Te$t Plan ”Xlli-D . . . . . .Test Plan XIV-D . . . . . . .Test Plan XV-DTest Plan XVI-D . . . . . . . . . . . . . .Test Plan XV1l-D . . . . . . . . . . . . . . .
Test Plan XIX-D . . . . . . .‘lest Plan XX-D
Tes\Plan XXI-DTest Plan XVllI-D . . . . .Bounda~line cri!eriun for rejet~ -accept decision .All Equipment lestplan derived from Tesl Plan I-DAll Equipment teslplan derived from Test Plan II-DAIIEquipment leslplan dertved frOm Tes:Plan 111.D
All Equipment lest plan derived from Test Plan IV. DAll Equipment leslplan derived from Test Plan V-DAll Equipment te>lplan deri.ed from Test Plan W-DAll Equipmenl!est planderived frOm Tes3Plan Vii-DAll Equipment testplan der, vedf<om Tesl Plan Vlll-DTime truncauon( lypelcen%or, ng)Combnned envlronmenta( lest profkle for fixed.groundequipment
Combined env, ronmenlal Ie$t prof,le for mobile groundequipment . . . . . .
Naval Wrfa<e Crak, mtssion enwronmenlal profde $or
externally mounled equipmenl(cold cycle).Naval surface craft, mwion enwronmental profile for
externally mounted equipment (hot cycle)Naval surface CfafI, M#SiOrT efWi10nr_IW71a1 profile for
imernally mounted equ!pmenl (cold cycle)Naval surface crab, miwon env, ronmenl~l profile fori nterna!ly mounted equipment (hot cycle)Naval surface Craft, miss, on enwronmental profile forinternally mounted temperature controlled
Naval surface craft, m,s%ion environmental profile forinternally mounted temperature comrolled
Surface craft and submarine vibration spectrumSubmarine pro file . . . . . . . . . . . . . . .Combined environmental test profile, for marine craftequipment . . . . . . . . . . . . . . . . .
General mission profile and characteristic for sixaircraft types and twelve m,wons
General mismon profile and characteristic! for sixa!rcrafl typei and Iwelve mt$~!ons
Genera! miwon prof,le and characteristics for fouraircraft types and seven m,s%ions
General mts%ion profole and characteristics for an
attach aircraft ona high.low.low-h,ghmtsslon
Page
218220222
22422622a230
232234
236/237238240242
244
246248250
252254
255
256
257
258
259
260
261
262
263264
26s
266
268
270
272
x
Page
I
I
.
FIGURE
61
62
63646566676659
70717273
-te7576
777879808182
83
M85068788899091
92939495%97
9899100101,Q
103106
10s
General mission profile and characteristics for afighter air~rafl cm an intercept mission
General mission profile and characteri$ticf fOr a,econna; y=r,:e ~~cr=f~ ofi a hiqh+upemonic mis5i0n
Mis$ion profile for temperature rate of cha~e calculaliOnDynamic ~rewre (q) as function of Mach number and altitudeRa”dOm vibration tesl envelope. for jet aircrafi
Environmental profile (example)
Missionpi6f;:=f?~~~cPJe)
Teap:Ofite(=amPle!Attack aircrafl test priflte ( 10w-lOw-lOw)
Attack a,rcra~tesl prOfile (clOse$up~n)Attack aircrah test prOfile (hi9h-10w”hlgh)
;+.h!gh.high)Attack aircraft test pro~tle (h.=.~t:ack ~,rc:ep. !eg p,ofile (h, gh-low40w. hi9h)
Af!ack atrcrafl iestorOfile(ferry) :ASW al,craft teSI profile (contact investigation - h19h)ASW ~,rcrah IeSI profile (contacl investigation intermediate).
Asw a,rcrahlesl prOfile(mln?lafi@*YVV ~ircrap, ;eil ~:cf{!e (h:gh.high. high!.
ASW Z,r<ratl tesl profile (search and attack).
ASW aircrah te$l Profile (surface ‘Surveillance)ASW alrCtaf LteSt PrOflle(ferry).
EcM alrcra~t e~tpfOfiie( penefrat;or~
ECM alrcraf~ ~e~,Pr~!;l@ @tJnd-Of~EC~wl~ir::af~~e$~pfQf!lP(f@rr~)
Flghler aircrafi test PrOfile (high-hi9h-high).F,ghter aircraft lest pro flh?(escoti).flghler air<ratlte$t profile (a, r deiense and capiive ti~gfi,i).
FighWr afircrati 1e51PrOiiie @;er~eWL).;ighter aircrak :EW wfile (high-[ ow-low”high)F,ghler aircrafi tes~ PrOfile (Iow-lOw-lOw)Fighter aircfati test prOfile (10w.10w-hi9h)
Fighler a,~crah te$t PrOfile (cl~e $“pWn)Fighter airc,af! te$t proiiie (ferry).
. ..,.-.fila /high-l@w-high!Reco””aistii,ce aircratt W%. p.- ..-.
Reconnaissance air~rafi test prOfile [lOw-10w’h’gh)Reconnaissance aircrafi test PrOfile (low-lOw-lOw) :
Reconnaissance airc~afi test prOfile (high-$ uper$On’cJ ‘Reconnaissance aircrah tes1 PrOiiie (hi9h.QJb@ic;ReC0nna15SanCe aircrafi tes: FJr6fi:~ ffe:w)Ta”ke, ai,craft Iest profile (high-low.high refuel).Tanker a,rcraft {low-low-low refuel).
Tanke, aircrafl le$lprofile (%trikerefuel)
COmpOsilelesl prOfi@(example)Compos,lelesl pro file(example)
Type A VfiTOL airborne early warnln9 miS~lOn PrOfile
272
273273274
215
276277278
27’32s0201282
283
2&4~g~
286287
288-@290291292
293
294295296297298299366
301302
303
304305306
307308
309310311
312
313
314
315
I
xi
MIL-HDBK-781
CONTENTS (Continued)
FIGuRE
106107
108109110111112
113114
115
116
I117
118119120121
I I 22
123
124
12s
126127
128
129
130
~
131
I 132
133
134
135
Type A VSTOL anti-wbmarine warfare mis~ion profileType A VfSTOL contact investigation mi$!ion profile
Type A VtSTOL marine a$$ault mission profile .Type A VE.TOL wrface attack mission profileType A V/STOL tanker mission profileType AV/5TOLveflica! onboard delivew rnis;on profileType B V/STOL combat air patrol mision profileType B V/5TOL deck launched intercept mi$sion profileType B VfiTOL subsonic nmface NHVeillance missionprofiles . . . . . . . . . . . . . . . . . .
Type A V/STOL airborne early warning environmentalpro file, . . . . . . . . . . . . . .
Type A VfSTOL anti-submarine warfare environmentalpro files .,, . .. ~... . . . . . . . .
Type A V/5TOL contact investigation environmentalpr0ftle5, . . . . . . . . . . . . . . . . .
Type AV/STOL marine as$ault environmental prOfileType AVISTOL surface altackenvirOnmenta fprOfile.
Type AVISTOL tanker environmental profile
Type A VISTOL venical onboard delivery environmentalprofiles.
Type BV/5TOL combalair paNolenvironment profileType B VISTOL deck lwnched mtercepl environmentalprofiles, . .
Type B V/STOL sub$onic surface surveillance environmental
profiles. . , .Turbopropeller vibration test spectra forequipment mounted within lhefuselage (example)
Thermal pro file forturbopropeller aircvaflTypical mission test cycle pro ffile
Combined environmental test profile for rolarywingaircrah .
Combined mission profile for rotary wing aircrak(hot andcold dayoperation) . .
Typical reliability captive flight test sequence(onecycle). . . . . .
Typical reliability free flight test sequence(onecycle) . . . . .
Random vibration maximum predicted ~nvi,o”ment forcombined air-launched weapons and as!embledexternalslores .
Random vibration maximum predicted environment for
air-to-surf ace(AGM) air-l aunched weapons
Random vibration maximum predicled environment foralr-to.ai r{ AAM)air-l aLInched weapons
Assembled external $tures and a,r.launched weapons -vi bra[ional reiponte accelerate on PSD versus frequencyspeclra
. . . . .. . . . .
..
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.,..
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Page
315316
316317317318318319
319
320
320
321321322
322
323;~j
324
324
325
326
327
328
329
330
331
332
333
334
335
.
.
xii
MIL-HDBK-781
cONTENTS (Continued)
Page
I
FIGuRE
136
137
138
139140141
142
143
144
14s
146
1b?
148
149
150151152153
Equipment installed in amembled ●xternal stores andair-launched weapons - vibrational refponae acceleration
noversus frquencyspectraInduced buffet maneuver random vibration response
spectrum . . . . . . . . . . . . . . . . . . . . . .Low- low free-flight mimion profile (example)Environmental engineering program KhemalicLogistics functional schematic diagramEuropean scenario assumed maintenance
$chedule and po$$ible operational utilization rate forenvironmental analfie} (example)
Target movement timeline for ●nvironmental
design criteria (European scenario) - largequantities (example) . . . . . . . . . .
Estimated percentage of time distribution for
lranspoflalion, holdldelay, and handling, fornominal .probable factory-to-theater movement
beeline . . . . . . . . . . . . . .Assumed typical attack aircrafi operating envelope
[standard day) showing the a~$umedhigh. medium.low mlmonprofile
Assumed typical attack aircrafi operating ●nvelope
(standard day) showing the assumedh,gh.low-h,gh mis~ion profile
Vibrauon faclor (g,”, (OVL))~ flight missiofl
profile high-medium-low use with FIGu RE5 130 and 143
except(”), verw$minimum g,~, (OVL)~(elample)Vibration factor (g, ~$ (OVL))~ fhght missionprofile high-low-high use with FIGURES 130 and 144
except (“), versus MiniI’IWm (g,,m (OVL))? (example)Store free. fitght vibration facwr
(g,~, (OVL))2 flight mis~iOn PrOflle IOW-IOW USewith FIGURES 131 thru 134 and TABLE 4B(example)
Unit-grm, (OVL)-acceleration P5D
verws frequency spectra . .Vibration profile$ for rail transportationRail transpofiationtest profileProgram listing for FORTMN programProgram listing for FORTWN program
336
337338
339340
341
341
344
345
347
349
350
351
352
354355356
358
xiiifiiv
. . .. .. ... .- .-— ___ _____ ___ .
MIL-HDE!K-781
1. SCOPE
1.1 -. Thi$ handbook provides test methods, test plans, and test enwronmenlal pro f,leswhich can be used ,n reliabtltty Iest, ng dur#ng the development, qualification. and producuon of systemsand equipment
1,2 Acml,cabilitf Th,s handbook ●xplaim techniques for use in reliability test% performed during Iheimegraled lest programs $pecil,ed in MI L-STO-785. Procedures. plans, and environments which can be usedm Reliability DevelopmentiGrowth Tests (RD/GT), Reliability Qualification Tesls (RC)T), and PfoduclionReliability Acceptance Tests (PRAT) arediscus$ed. In addition, Environmental Stress Screening (ESSI methodsare provided.
1.2,1 APII Iicatmn of handbook. Data provided inthk handbook can ba u$ed $eIeclively on reliability
te$t program~ and can be \pecifted m Depanmem o! Defense contracted prctcutements, reques!s forpropo~al$. statement$ of work. and Government in-houw development wh,ch reqwre reliability testing
1.2.2 Tailorinq. The data provided herein can be selected for use on tailored reliability test programsas reQu# red by govern, ng regulauons and as appropriate 10 the particular system or equtpmenl, tintended
aPPl, Cation, Pr09ram lYPe, magnitude, and funding,
1.3 Method of refeten<e When referencing the lest methods, test plans. and environmental lestconditions of thts hand booh, the handbook and the fpecific paragraph number(s) are 10 be rated
1.4 Equ, preen\ ca!eqornes The methods in this handbook are apPhcable 10 SIXbroad calegones ofequipment, dlst, ngufshee accord, ng to each equipment’s field $arvice applicatmn:
Calegory 1
Category 2
Category 3
Category 4.
Calegory 5
Calegory 6.
F,,ed.grcwnd equipmenl
Mobile ground equipmemA Wheeled vehicleB Tracked .eh, cleC. Sheller con f,gurat, onD. Manpack
Shipboard equipmenlA. Naval surface craftB Naval submarineC Mar!ne crafiD Underwater vefwcle
Eqwpment for jet aircratiA. Ft,ed-wingB vertical and Shorl Takeoff and Landing (v/5TOL)
Turboprop aircrah and helicopter ●quipmentA TwbopropE Hel Kop:er
Ml$sile$ and assembled external $mresA A,r.launched miwlesB Assembled elternal storesC. Ground.launched mmiles
1
MIL-HDBK-781
2. REFEflENCF D():LJMENTS
2 I ~v.e~!a!nen! documen!>
2..1.”! Soecbfocat,on%, standard~, and handbooks Unless olherw!se SPeclf, ed. the followongspe,.iff cation%, standard%, and handbooks of the Issue hsled In the Department of Defense Indes ofSpecifocatlom and Standards (DODISS) and ,1s supplements specif, ed m the solicllatmn form a par! of Ih, $documer,t to the exk’ol specifted herein.
SPECIFIuTIONS
MILITARY
MIL. E-5400MIL-E-605!MIL-P-9024
STANDARDS
MILITARY
MIL.STD-167-1
MIL-STD-21OMIL.STO-280MIL.STD-461
MILSTD.648MIL.STD.721
MII .s1 0-781
~,, L.5TD.785
MIL.STD-81OMIL-STD.1385
MI L-STD.2164MIL.STD-45662
HANDBOOKS
MILITARY
MI L-HDBK.189MI L. HDBK-237
MIL.HDBK.2S3
Electronic Equjpmenl, Aero$pace, General Specifocauon ForElectromagnetic Compatibilny Requirement For SystemsPackaging. Materials Handling And Trampoflab!lity, SyJtem And SyslemSegmenw General Specification For
Mechanical Vibrations of Shipboard Equipment (Type I - Environmental hndType II. Internally ExctledlCl,maltc Extremes For M,lllary EqubpmentDe flnil,om Of Item Levels, Item E,changeabilily. Model%. And Related TermsElectromagnetic Em, won 4nd 5u5ceplab,l, ty 17equlrements For The ControlOf Electrc.magnel, c InterferenceDes, gnCr, te, +a For Speclall?ed Sh#pping Contaoner%De{, n,t, omUf Etlect, ven,:$%le(, tl\ For Rel, ab,llly. Matntatnab,l, ty, HumanFaclors, And SafetyReltab,l!ty Te$l, ng For Eny, neermg Development. CJual, focal, on, AndProducuonRel(ab,l,iy Program For 5y!1em\ And Equipment Development AnaProducuonEnvironmemal Teit Melhnd% And Engineering Gwdeline$Preclus, on Of Ordnance Hazard% lnElectromagnetlc F#elds, Gener~’Requirements ForEnwronmental Stress Screening Process For Electronic EquipmentCal#bra!ton System Requtremenl>
Reltab,lnly Growlh ManagemenlEleclromagnet,c Compatib,llty Management Gutde For platforms, SystemsAnd EquipmentGwoanre For The Des,gn And Tesl Of Sy$tem* Protected Against The Effecl\Of Electtomagnet,c Energy
2
I .
MIL-HDBK-781
2.1.2 Other Governme~t documents The following other Government documents form a part of Ih,ihandbook m the ealent spec, f#ed here, n
PuBLICATIONS
NAVAL AIR SYSTEMS COMMAND (NAVAIR)
AR70.38 Reiearch. Development, lest And Evaluation Of Material Far E.lremeChmatic Conditions
AD.lll S Electromagnetic Compatibility Design Guide For Avionic$ And RelatedGround SuppcIrt
(Copies of specifications. standard$. handbooks, and publications required by contractors in connection withspecific procurement functions should be obtained from the procuring activity or a! directed by thecontracting of ficer.)
I
..
I 3
MIL-HDBK-781
3 UFFINITION\
3 \ ~ Term> used herein arein accordance with l&wdef, nitlons in MI L.5TD.2Lf0, MI L. STD.721,iv:,, ,. TO.785. MI L-STD-81O. and MI L-HDSK-189, w,lh the Pxcept, on andadd, uon of Ihetermsspecafoed O.~ I ! through3 1,9.
3.1. \ Contractor. Contraaor includes Governmental or ,ndustnal acthwl,es developing or producang{nliitary sys!ems and equipment.
3.1.2 Corrective n,aintenance (reoair]. The acciom performed, as a result o{ failure. to reslore an,Iem to a specified cendiuon
3.1.3 Decision r,$k$ Deci!ion ri$ks shall be as fpecified in 3.1.3.1 through 3.1.3.3.
3.1.3.1 Consumer’s risk @. Consumer”% risk (&) i$ the probability of accepting equipment whichhe! a true n!ean-lime.&lween-fa,lure (MTBF) equal 10 the lower te$I MT8F (01 ), The p,obab(l,ty ofaccepting equipment which ha~ a lrue MTBF less than the lower ?%1 h4TklF (o, ) will be Ie!$ than @)
3.1.3.2 Producer”$rtsk (~ Producer’s risk (CY) IS the probabllltyof refecungequipment which ha> atrue MTBF equal to the upper lest MTBF (8D ) The probability of rejecl, ng eqtopmenl wh, ch has a lrueMTSF greater than the upper test MT8F (L90 ) w,II be less than (a)
3.1.3,3 C%<riminaiion ratm (d!. The dmcrimmation ral,o (d) usone of the standard lest planparameters; it osthe ratio of the upper tesl MTBF (80) 10 Ihe Iowertesl MTBF fe, ): lhat is, d . C?UI0..
3.1.4 _ Failure iypesand clas$ii!ca(ion$ arespec, iled In MIL.5TD.721, wtththe ezcepl)onoimultiple, paltern, and chargeable fa,lureswhnchare $per,l, ed ,$. : ~ 4 1 through 3 1.43
3.1.4.1 Multiple failure% Mull,ple fa,lu!es are !he wmultaneous occurrence of IWO or moreindependent fatlures When two or more faded parts ale found durtng lrouble$hoollflg and Iaolure$ csnn6:be \hown 10 be dependefll. mul!lple fa!lures are prmumed to have occurred,
3 ~.d.2 Pattern fa,lures The occurrence of IWO or more Ia,lure%of the%ame pan #n ,dent, cal o.equ$valenl applucatoons when Ihe fa,lures are cau%ed by the same bawc failure mechanwm ano the teIlu#esoccur M a rale wh,ch n tnconsislenl wnh the pan”% predlcled fa!lure ra!e
3 1 4.3 Chargeable failure Arelevanl, Independent failure of equ,pment under test and anyCfependent failure$cau%ed lhereby wh, chareclasmi, eo a%one ia,lure and used todelermine contractualcompfaance with acceptance and reject, on criteria
3 1.5 Independent! chargeable fa,lure caleaorte$ Fa,luresdef, ned, n 3.1 5.1 lhrough 3 1 55 arecategorized as independent chargeable Ia$lures
3 1.S 1 Eauipment des,qn fa,lure Any Ia,lure wh,ch can be traced dmectly 10 the des$gn of theequspmenl; that ,s. the des#gn of the equtpment caused lhe part tn questoon to degrade or fall. rewlttcg tnanequ, pmenl failure
3.1.5.2 Eau,pmenl manufaclunno failure A failure wh,ch i$caused by poor workmanship orfinadequ ale ma”ufactur,”g process conl, ol d“r, ng equipment construction. Iestlng, Or ,epalr Prl Or 10 Iheslar! of testing: for example, the failure of an ai$embly d“e to cold solder jmnls
3.1.5.3 PandeS!Qn fa,lure The fajlureof pans wh!ch can be traced d,reclly loonadequatedes,gn
3.1.54 pan Manufaclurtna failure Parl fa,lureswh+<h are the rewllof poor workmanship orinadequate manufacturing process control dur, ng par{ assembly, tinad equate nnspecl, on, or Improper
te51tng
3 1 55 So flwa~e erro, fa,lure k fa, ture caused by an error inlhe computer pro$~am a%so<$ated wtnthe hardware
4
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MIL-HDBK-781
3 1 6 Meawrwol rel+abil, tt Reliability measurement shall be as speofhed !n 3 16.1 through 3 1.69
3 1.6.1 Demonstrated f4TBF interval (8 d I Demon$tralid MTBF irnerval (@d ] is the probable range
of true MTBF under lest cond,l, ens; that I%,an interval e518mate of MTBF al a stated conlldence level
3. 1.6.2 Observed MTff F (j). Observed MTBF [j) is equal to the total operating time of theequipmem divided by the number of relevant failures.
3.1.6.3 Lower test MTE~ (c?L). .Lower tesl MTBF W! ) it that value which ii unacceptable. The$tandard test plans will reject. with high probability, ●quipment with a true MTBF lhat approached (f?, )
d~,r,.i..ti..ra~3.1.6.4 Upper test MTBF f ). Upper test MTBF (L70) is an acceptable value of MTBF ●qual to thet!me$ the lower te$t MTBF (& ). The !tandard test plans WIII accept, witn high
probability, equipment with a true MTBF that approached (@.), This value (00) shall be realistically
alla, nable, based on experience and ,nformali on.
3.1.6.5 Predicled MTBF (6’Q). Pred!ded MTBF (OP ) i$ that value of MTBF determined by reliabilitypred, cuon method%. tit asa {unctmn of the equtpmetm design and the uce environment. (&P) should beequal 10 or greater than (8U ) in value. to ensure with high probability, that the ●quipment will be acceptedduring the reloabollly qual, f,cation lest.
31.6.6 Ob$er.ed cumulali.e failure rate (P(t)l. The observed cumulative failure rate (P(t)) at time (t)I%equal to the number of relevant system Iailurei N(t) accumulated by (t), divided by (I).
3.1 6.7 Intensitv function (P(t)) The intensity function (P(t)) i$ the change per unot lime of theexpected value of N(t), the number of system failure$ muluplled by time (t). This is writlen as:
P(i) = dE(N(t))/d!
where E ,epre%ent% the expected value
3. 1.6.B hmtamaneous MT8~ function (M(t)). The instantaneous MTBF function at (t) is equal to thereciprocal of the failure rate {unclmn.
3 1.6.9 Ob$er.ed reltabil,tv (R(t)) A point eslimale 0( reliability equal to the probabfl, [y of survivalfor a $pecif, ed operaling !tme. (1). g,ven that the equipment was OpwaliOnal at the beginmng of the per80d
31.7 Mission orof,le A genenc definition is specified on MIL-STD.72 I Thi$ ampliflcal,on of thatde ftnitqon appltes 10 rel,abilily test programs. A thorough description of all of the major planned events andcond, t,c.ns associated with one spec,fbc miwon. A mission profile is one ~gment of a Ii{e-cycle prof#le (for
example. a mil$ile caplive. carry phase or a miisile free-f ligh: pha$e). The profile depicti the Ilme \pan of theevent, the expected enwmnmental Cond, tmns, energized and nonenergized periods, and so fonh.
3.1 B Life-cvcle orofile A thorough time-life description of the events and conditions a5socoaled withan item of equipment from the lime of f,nal factory acceptance unlil its ultimate dispositmn (for example,facxo,y.to.target sequence) Each significam life-cycle event. such as tran$pofiation. dormant storage, te%land checkout. standby and ,eady modes, operational deployment. and mission profiles, #saddressed.
includbng alternate po$!, bil, ues The profile depicts the time span of each event. the environmental
conditions, and lhe operating modes
3 1 9 Procur#nq acl,. (ty As used on Ih, s handbook, procuring ac[tvily refers to a Government agencyor toa prime contractor on tran%acuomwtth itswppl, en
5
MIL-HDBK-781
4 RELIABILITY TEST METHOOSANDTEST PLAN5
4.1 -. Section 4 provides information and gwdance tor Y?lecIing the Iesl melhods and Ies..plans required 10 implemeni the left program~ specif}ed in MIL.STD-7E1
4.1.1 ~. Section 4 provides test method% and test plans which can be used when performing the
reliability test programs $pecified tn Task\ 200.300, and 400 of MI L-STD.7E1. Methods are provided for
e.aluatincl data Drocfuced durina RDIGT and ESSDroaram$. lest Dlans are Drovided for MTBF assurance andfixed-d ur;!ion aid sequential re;iabili!y demons~ral;on and awe;srnent le~ts and all-equipment reliabilityiestk Thaw test plain can ba selected for u$e in ROT and PWT.
..
4.1.2 Agolications matrix, The interrelation$hip~ between the test methods and test plans describedherein and the tasks $pacified in MIL-STD-7BI are provided in TABLE 1.
4.1.3 Test methods Methods for evaluating reliability growth during RD/GT and for evaluating ESS
programs are provided in4.1.3.l and 4.1.3.2.
4.1.3.1 Growlh monitor!na method Two growth momloring (data evaluation) methods are
described: the Duane Method and the Army Material Systemf Analysis Agency (AMSMJ Method TheDuane Method is a graphical and nonstatistical technique which can be used 10 graphically plot changes inreliability. The AMSAA Melhod is based on Ihe a}wmphcm that the time> between successive failures ca” bemodeled as the intensity funct, on of a nonimmogeneow Poisson process. Th!$ ,mensity f“ncuon isexpre;%ed a$ a Mult!ple of the cumula18ve Ie$t tame raised 10 wme power. The Ouane and AMSm methodsare described in MIL-HDBK.1B9
4.1.32 ESS evaluation methods Two ESSevaluat#on melhods are described which prowde a meam
to determine when the ESS procetiure should be terminated One of the methods provides a techn,que forcalculating a required ESS time Interval (which must be $au$f,ed 10 $IOP screening) prior to the slarf of Ihe
ESS The second method make% use of arbitrary Inmes based on hmlor,cal data.
4. 1.4 Test plarm MTBF ajwrance Iesl$ and the f,.andard test plan, provide a wide selection of Ieits
suitable for tailoring IO conform 10 the requirements of any rel#abillty program
4. 1.4,1 MTBF aswrzmce lesl$ The MTBF asswance Iesll we a failure-free interval concept 10 ver, ff
MTBF. Thetestsprowde ades!reo ajwrance Ihal a mln!mum specifoed MTBF level i$achleved inadditnon toprovidang assurance thal early defect failures have been eliminated This test can be used on production
equipments which have prewoudy pa%sed qualnflcatton tewng The MTBF assurance :e>t provides theproducef with a high probability of wccess.
4.1.4.2 Stzmdmd test olans The standard lesl plans conta, n slalist!cal criteria for deIerm8nungC0mp18a~Ce w,th spectif,ed rehabillty requtremenl$ and are based on the assumption that the underlyingdistribution of tnme+belween-fail ures ISexponential The exponential assumption impltes a constant fa)lurerate; therefore, thew test plans cannot be used for the purpose of el)minat$ng design defects or infantmortality failures The standard tell plans are as categorized In a through d:
a. Probability Ratio Sequential Test plans (PRST) (Test Plain I-O through VI-D)b. Shon-run h!gh.r!sk PRST plans (Test Plans VII-O and VIII-D)c. Ftxed-duratmn lest plans (Test Plain IX-O through XVII-D and XIX-O through XXI. D)d. Ail-equipment reliab!hcy te$l plan (Test Plan XVIII-O)
These statistical test plans are to be used to determine contractual compliance with pre-e$tabl!shed accep!.reject criteraa and should not be used m project equ$pme”t MTa F
~
4.2 lest method and tesI elan selectnon factor% The rnOSI important factors to be c.anmdetee when
selecl, ng an approprna!e lest plan or method are prowded tin 42.1 through 422 S
I 4.2 1 Tesl method and te%! elan selection Thelejl rnethod%and te%: plans to be uwd in RD:GT, RQ7,
PRA?, and ESSshall be selected from lrw malerml prowded m a Ih,ough f The test melhom or lest plans
6
. . . . . .._ ~ — —. ..- .. .._-_—_
MIL-HDBK-781
$hould be specified fin the contracl and Ihe equlpmenl specification and described. an delatl, ,n the reliabilitytest plan document.
a. The rel!abil!ty grotih monitoring method should be selected under condtuom whereparameters of the ume-to-failure d,stributmn are ●xpected 10 be changing with t#me.
b. The ESSmethods are 10 ba wed to eliminate ●arly defecu (infant morcalily). The StandardEnvironmental Streis Screen i$ a form of ESSused when ic muff be verifkd that equipn%en!, which has passedprevious reliability testing, has not been degraded by the production process
c. The MTBf as$urance I-I can be used to provide assurance that a minimum specifwd MTBFhas been achieved and that early defect failure$ have been ●laminated.
d. A flaed-duration lest plan must ba aelecced when it i$ necc.fmry to obtain an estimate of thetrue MTBF demonstrated by the lest, as well a%an accept-reject decision, or when total test lime must beknown in advance.
e. A sequential lest plan maybe aelectad when it is desired toaccepl or reject predeterminedMTBF values (eO. @!) with predetermined risks of error (ca~). and when uncertainty in total test ome isrelatively unimportant. Tht$ lest will fave test lime, as compared 10 fJxed-du ration le$t plan$ having iimilarrisks and doscr, m,naticm ratio%, when the true MTBF is much greater than (@O) O, much less Ihe” (81]
f. The all.eqwpment test plan maybe selected when all units of the production run mustundergo a reliability lot acceptance test.
These Stau$tical lest plans are 10 be used to determine conlracluat compliance with pre. e$labtished accept-reject criteria and \hould not be used toproject equipment MTBF.
4.2.2 Tesl me:hod and te$l plan paramelerwlecoon. Themoslimponant pa~ametersmbe
considered when select, ng test methods and test plain are discussed in 4.2.2.1 through 4.22.5
4.22 1 Ectu,oment performance. The parameter! to be measured during reliability le%:i and the
applicable acceptance I!mtl% should be delermmed by the performance requirements of the equipmentdestgn control specif,cat,on ana should be included in the test procedures.
A.2 2.2 Equipment auamity lhe number of equipmenl 10 be \ested, not necessarily $,mullaneousby,
shall be aelerm$ned as described herein or as specified in the carnracl.
a Sample s,ze [reliab,l,ty growth andqualificat,on). The$ample vzerequired for thegrowlh and qua! tf,cat,on pha!e lest plain should be as spec!f,ed on the contractor as agreed to by Ihe
conwactor and the procur, ng acu., tyb. Sample $ize (production reliability acceptance). Unles$ olherw45e specif,ed by the
procuring acttwty, the mmimum o{ samples ta be tested per [ott% three p,eces al eqwpmenl. Therecommendeci Jample s;ze #s10 pewent of the equipment per 101. up 10a maximum of 20pieces of
eqwpment per lotc. All-equipment praductian reliability acceptance test. Under this Iesl plan. all producuon
equopment is subjecled to the rel!abtlity acceptance le5t. All-equipment acceptance Iesung (100 percentsample) should only be specif ted under exceptional circumstances. as determined by the requ, remenls af~fety or mosston success
d Sample $ize (ESS) Unless otherwise $pecif,ed by the procuring aCli.itY. ielected
development equipment and all equ,pment in production Iats should be wb]ected to ESS In h!gh volumeproduction runs, the sample sflze from each lot shauld be selected by the procuring activity. In,taal 101$
should be 5creened al lhe 100 percent level. Sample size on later lot> may be reduced by the procurtng
acttw:y baaed on the screening results.
e $ampiesize (opltonal nonstatistical te$l). The sample stze far1h#5 Iesl isal! equlpmenl tina lal whase ver,l, ed reliabil,ly charac(er!$ticj may be degraded by m.inufaclur, ng and qu.31f1ydefeC!>
7
1’””
MII.-HDBK-781
I
4215 1*.1 du,.+t, o,> Ttw test duratton for ftDIGTshou10 bespec, f,ed ,n advance, by Ihc.
bovemmer. t, 10 the request for proposal. contfacl, and spec, ftcah on, Dur, ng the test program, add, (,ona!test time may Ix> specif ted ,f needed lo achieve reliabi~!ty goal% ESS lime i$avar, able, wfmchdepencf son 1o,,size, fa,lure d,,.lrf bution 01 the early faiiures, types ofenvi tonmental >Iressappl, ed, and stress levels Somemaximum allo.v.lb[e lest tlme$hcwld he wed for test plann, ng For%equenlial lest plans, lest cfwat, or,should be plafi.wd on the baits of maxtmum allowable lest lame (truncation), rather than the expecteo
dectision poii~l, (o avoid the probability of ~~nplanned tesl cost and schedule overruns. Testing should
continue imt; i (he total UI18t hours together with the total COunt of relevam equipment failures permiteither am accepl or rejeci decision in accordance with the specified test plan. However. for the all.
equipment reliability test. testing should contanue until a reject decision is made or all contractually requiredequipment has been tested. Equipment ON time (that i% equipment Operating time) should be used to
determine ten duration and compliance with accept-reject criteria. Testing should be monitored so that thetimes of fai!ule may be recorded accurately. The monitoring instrumentation and techniques and themethod ofesbnating fiA7BF should be included in the proposed reliability test procedures. Each equipmenlshould operate al least one. hali the average operating lime of all ●quipmem on test. The duration of fixed-time tests should be speci {tied in the request for proposal, contract. and equipment specification. Thus testduration should be the max, mum allowed by the schedule and l,scal constraints of the program.
4.2.24 Deciwon ris}, > Theconsurner’snsh (fS) i$ the probabiltly lhatequtpmentwilh MTBF equa! :0
the lower test MTBF WIII be accepted by the test plan. The producer’s risk(a) 15the probability Ihatequipments with MTBF equal to the upper test MTBF will be rejected by the test plan. In general. the use oflow deckion ri~ks will resull In longer test I,me However. low dec, s,on nsk$ prowde protection aga, nit therejecu. a” O( satisfactory equipment or acceptance of unsatisfactory equ, pmenl For each of the truncatedsequential plain (PRST), the ezact nskswe, e calculated. ShifKsi” the accep[. reject I,nesa”d truncation po, mswere made to bring the True ,isks closer 10 the dewgnated risk~ and 10 make the two risks more nearly equalIoreach plan Thedecis, on nsksof the all-equipment rellab,litytest vary w,lh the lolal teslt!meancf have!AtIle ~ig,),ft<ance .?! ,><cason forchoos!ng thss plan
4? > 5 >,%t,#,o,ondt,o,~.tilau di I The d,scr, m,nation ralio (d) M the rallo 01 the upper Iesl MTBF( 80) to tile lower test MTBF (6’:) and Isa measure of the power of the te%llo reacha decision qu, cklyand,together w,th the dec, saon risks, define a sequential tesis accept-reject crtiteria In general, the hsgher the
d,scriminat, on ralto (d), the shoner the lest The dtscrim, nalion rauo (d) (and corresponding lesl p!an) m~slhc chosen carefully 10 pre.enl the resulung (@O)from becoming unalminable due to de$ign I,tn,lat,on$
.I 7 Rel, abilitv DevelopmenUGrov.nh Evaluation Methods
a. The Duane Mel hod was originally developed by J. T. Duane ($ee Reference 1). Thns methodmake> use of a graphical and non%tat,$t,cal technique wh!ch provides a p,clorial presentation of the changes
occurring In the measu reti rel!ab, hty parameter. Numerical estimales of the reliability parameler also can beobtained.
b The AMSAA Melhod for evaluating reliability growth presented here#n was developed byAMSAA. Th, i method t> d,scussed ,n some deta!l in MIL-HDBK-189. Additional ,nformattcm is prowded !nReference 2, The AMSAA model was selected for inclusion In thi$ handbook becauw it is an analyucal modei
which permits confidence interval est, males to be computed from the test data fof current and future valuesof reliability (MTBF) or failure raie (k), In addition, the model can be applied to wther conwmmus (ume) or
discrete (rounds. roiled reliab,lnly systems. single or multiple systems, and testf which are time or failure
truncated
4.3.1 The Duane Method. The Duane Method is a graphical technique which is useful in the analystsof reliability growlh data. The :echn,que is quick, simple. and easy to understand The Duane plot or graphcan dep!ct facts that may be h!dden by a purely $lalmt!cal analysis For example, a goodness. of. flt Ies! maycalf for rejecting the AIVISAA mocJe!, but VVIII “c,t ,“d!cate pombfe reasons for che ,eject’on A plot of the
same data may find, cate some reason for the problem, Howevev. (he rel, abil,ly parameter> cannot be
estimaled by the Duane Method aswell a$ they can by a $talIshcal model and, of course, no ,r.ter. ai
8
MIL-HDBK-781
I
.
esl, mates can recomputed lnadd#l, on, the Duane plot uses a%traight line which is ftltedby eyetothedalapoints. Thegraphtcal andstat, st, calmethods should beviewed ascomplemenlary techniques
43 1.1 ~ The%ymbols used, nlheequat, On$oflhe Duane Melhod are:
C(t) = expected number oflailures in(l) un,t$ofdevelOpment lesl,ng dtivided by(t)
f(i) = eapected numhcof failures in(t) units ofdeveJopmenl te$1ing
m = dOpe Oflhe Duane plOt
* = reciprocal of theordinate of the Duane plolat(t) = 1
e(() = current MTBF
r(t) = current failure rate
~ = a.erage failure rateofgrouped datainintemal(i)
4.3 1.2 Construct, onofa Duane olot The Duane plotcan ticon$trucled asspecifted inathroughg:
a. The Duane model can reexpressed in the form:
c(l)= Al-”’
where:
c,,) . y
Since (F(I)) 15Ihe expected number of failures experienced by the sy5tem during (t) units of developmentIe\ling, it can be e$timated by (N(t)), the observed number of failures during (1) units. Therefore,
Iv(()/( . .\ I - “
usthe observed relationship. Thrs may be expressed as a linear relationship. suitable for plotting, by takingIogar!Ihms
ln(h’(f)lfl = (n(k)– m In(l)
However. since il is easier m wsualize growth a%an upward doping line. a more commonly used reta:lonship
is:
ln(Uh’(0) = m 1.[!1 - In (A )
b. As the Iest#ng progresses. record is kept of (1), Ihe total units of operation accumulatedamong all the systems Thus, !f three systems have been tested for 100 hours each, t = 300 Record alio ISkept of (N(l)), the cumulative number of failure! experienced during the (t) units of OPeralion.
c. Al selected .alue% of (1), the quantily (UN(1)) is computed.d. .Uvng full-log graph paper, the value$ of (t) and (UN(1)) are plotted on the ab$o$$a and
ordlnale, respectively
e If Ihe plolted po!nts form a rea$onably$tra, ghl I,ne. II can be concluded Ihal lhe Duanemode! ,$ & reamnable me!hod for tiescrtb, ng the growth pattern observed
f After f,tt, nga $ua, ghl Ilne through these po, nls, (), ) may be esltmaled bylhe reC@ro;alof the orddnate al(t)= 1 The paramele, (m) maybe estimated by Ihearnlhmel!c slope of Ihel, ne Each
9
MIL-HDBK-781
successive point contains all the in fcwna toon contained in earlier points. Therefore. the most recent po,ntsshould be given heavie$t weight in plol. ung the lane.
9. An e$timate may be made of the current value% oi MTBF (f?(u) and the iatlure rate (r(t)),
by means of the relationships:
G(i) - im/(i - m)k
and
Any ●xtrapolations beyond the test period are Sen$itive to the a5SumPU0n of using the Guane mOdCl, andme-a ..,* ~swi.mmal S55U%P4WOU.8,-. ..,= ~,q, . .. . . . . . I. o rem.t.. . . . ..-1. .I. -.+ 4... . . . . . h-., .h - .,.-,.,” ++ ,. ~ =.’- r-mctant i“ the ●!?s~,i.ng pened, The
●nalfiis of data from several identical $ystemi being tefted simultaneously may be complicated by (he factthat d-ign modifications may not be introduced on all $fitem~ simultaneously. This will result in a mixtureof configuration ages wtiIcn wiii make data anaifiis more aifficuii
4,3.1.3 Ezamole. As an ●xample, three systems were teswd simultaneously until a Iolal of
1000 hours of operation was accumulated among the Ihree $y$tem$. As failure! occurred, appropriate
design modifications were introduced on all three symems. The cumulative number of failures encomferedafler selected peraods of testing and the Corresponding vaiues of iu”Nii)) are given beiow:
N(I) UN(1)(hundred~of hours) —.
1.00 3 0.3332.00 6 0.3335.00 !3 03135
8.00 18 0.44410.00 22 0.454
The MaIue$ of (1) and (1/N(tjj a,e ihowm piotle.j in iiGURE 1. The points form a reasonably straighi i!fle,
suggesting thal the Duane model ISappropriate for describing Ihe glOWth pattern observed. A straight l#neis then f!!!ed ~.hrough th?s? poinw
The ord$nate at (t) = 1 1s0.31. Therefore. ).= 1/0.31 = 3.22 Thear#thmetic slopem = 15 milltmelers(mml
divided by 95 mm = 0.1SS. This may ai$o be determined by:
fn(o .445) - ;fi:o.3; o) _ 0,,57m.
in[l Gj – in(l) –
The MTBF curretwly achieved a! 1000 hours may be esiimated as:
, 0 +0.::?e(!~o~) . = 0.52 SSAu.ndmdhoum = 52.813 hOUI%
(1 - 0.157)(3.22)
and ihe current failure rate may be estimated as:
r(li2@2j = (; - 0.;57 )(3.22) iO+.:$~ = i .8% fuiiutea per hundred hotirs
= 9.0; S9 {iiilures Fr hour
10
.
.
MIL-HDBK-7B1
The MTBF expected al 2000 hours maybe esumated as:
*O +0 1s7
e[2000) = = 0.5696 Aundrcd hours - 58.96 houm(1 -0. IS7K3.22)
This ●$timate assumes that the Duane model i$ valid for the growth pattern being ●xperienced and that theprogram effon is so remain constant.
4.3.1.4 Problem$ of olottina aviraae failure rate. One disadvantage of plots, such as the Duane plot
which us- cumulative measures, is the fact that the most recent data tends to get buried when it iscombined with all the previous data. Pkotting the averaga f?ilure rate of selected intervalf eliminates thisproblem. The lack of cumulative smoothing. however, does make the atierage failure-rate plot much moresensitive to sampling variation. The average failure-rate (AJ over anytime inlemal i$ the number Of faifufe$
in that interval (n) divided by the total operating time in the interval (TJ.
The choice of interval$ i! arbitrary, bul they should be small ●nough to reflect trends, yet large ●nough to
afford some $moothing. The average failure rate is plotted as a horizontal line for the appropriate interval.The test results used in the previous example are grouped into intervals and the average failure rate i!
computed for each imerval, that is:
Interval m i
f!s!m Number of failure% & \FaiIwes/hour~
0-100 3 100 0.0300100-200 3 100 0,0300
200-500 7 300 0.0233
500-800 s 300 0.0167
80& 1000 4 2’30 0.0200
A.erage failure rate over each interval is shown in FIGuRE 1; however. FIGuRE 2 provides a clearer picture ofthe trend.
4.3.2 The AM5~ Method. A wmmary of the variable$ used in the AMSAA model is given m
TABLE 2.
4.3.2.1 Determination of trend from test data. Prior to the use of the AMSAA method, any
significant trend ,n the test rewltl must be identified. Multiple sywem! should be analyzed on a cumulativetest duration ba~i! (time, mile$, and so forth) by combining the failure data on the multiple systems. as if Iheywere a Jingle $ystem, and then analymng the data as a single sywem. (f the period of observation ends
with a failure. use Ihe test statistic (/4 generated by equation 1 in TABLE 3. If the failure data is time-truncated, use lhe test statistic (P) generated by ●quation 2 in TABLE 3. At the 10 Percent (lw~~ided)
significance Ievel. g = 1.U5; therefore, if:
a. p S - t.645: Significant reliability g,owth is indicated at the 10 percem $ignif, cance Ie.e[
and the AMSAA model can be used for estimaung parameters of interestb p= + 1.645: Slgnif!canl relia~,l!ty decay t> indicated at the 10 percen! wgnif(cance level.
Corrective ac;ion IS necessary.c. - 1.64S <PC + 1.645: The trend i$ not significant! the 10 Pefcen1$19ni flcance level and
add, uonal data should be accumulated
11
.-p- “r c.”” --”,”= n-~-. ,~--,.-...a “ . ...” -- ”.-.
---,,!- -m -.”,.-.,.,.”” .A “m,l.. .m-. m , ~“. -.
MIL-HDBK-781
For value, near -1.645, some growth ii #nO,<ateii, for value near ●1.645, some decay is indicaled, for value~near zero. “o Trend i$ ,ndicaled Add!uc.nal tesung \hould be considered an these marg, nal cases
Other crit,cal values of the Ie$t statistic are:
Value Percent level of smnificance (two-sided)
-3.09 0.2
-2.S76 1.0
-2.326 2.0.1.960 5.0-1.W5 10.0
-1.282 20.0
In practice, higher critical values will result in more te$l time but will yield a higher confidence ef reliability
growth,
4.3.2.2 Reliabil!tva rowlh analv%, s. If significant growlh is tndica ted. compute the appropriateparameters using lhe reliability growth equations selected from TABLE 3. U$e TABLE 4 as a guide for
equation se~ection. Note that for small mmple s,zes. the recommended estimate of@ is the unbia$ed●s\imate, w). which is:
Fot failur~trun<ated {e$~, use equation 4
ii=[[N-2YNlt
and for tame-truncated tests, use equation 8
Tf=llN-lYNlj
The recommended ewimate of (1) is (1), which is:
and for lime-truncated tesIs:
i = N/f:
The goodne~wf-fil of the AMSAA model to [he particular lest data being generated must be lested by use
of the Cramer-von MIces goodness-o f-fli test. First, the level of significance (a) of the test must be chosen
and the critical value of the test Slat\$tic (C:) determined from TABLE 5. The (C:) calculated from lheobservations (equattons 6 and 10 In TABLE 3) mu$l then be compared to this crmcal value. If the $tauslic ISle~s than the tabulated critical value, the Ah4SAA model cannot be rejected and the calculaucm procedure on
steps a through g below can be used If the $talistic i$ greater than the tabulated critical value. then theAMSAA model ,s rejected If the model IS rejected, follow the procedures gtven in $tep h below,
a If the AMS% model !Sappropriate. the system inten$ity fwwlion may be estimated as a
funnionof time by:
44$.,;(l) = Apl (for large sampled
. .
p(ll = Xiii-‘ (for small sampled
12
.
MIL-HDBK-781
The ,nten$, ty funcl, on ,sequa! m theder!vatave. at l,me (t). of lheexpec!ed number O( failwestn the tinterval
(0,1)b Then calculate (&t)) or (6(O) al the end of the te$t (or at the po,nt ,n the test al which the
Catcuiatwm is being made)c. From TABLE 6 for failure. terminated test and from TABLE 7 for tome. terminated lest,
oblain the two-sided lower confidence bounds (LwY) and tw-sided upper confidence bounds (UN.YI for Nfailures and (Y) percent confidence coefficient.
d. Compute the inlerval estimate of MTBF from:
LNY U*,.Y
~ $MTBFs~
e. If the number of failurec if 20 or more, the wme percentile may be used to construct
approximate confidence bounds on the future MTBF.f. The MTBF is:
h; =1 /j(() (for large samples)
k) -1 I;(f) (for small mmples)
g From the co” f,dence limits on M(t) previously calculated. the corresponding tim,l$ for (1)
may be found from:
J’.b= “~lb
h. A poor Cramer-von Mtses ftt maybe caused by jumps or dtscont$nuiue% in lhe growth
pattern. A plot of the data may suggest whether a different, continuous model should be con$, dered: orwhether program changes, which may cause breaks in the growth pallern. should be invesltgated. When
there we lump% or d,$cont, nuil, es on the growth pattern, the AMSAA model may be applted on a piece-wl%efashion. The procedures are a! described in 4.3.2.2a through 4.3.2.2g. eacepl Ihal the data prior 10 andfollowing the ume of dn%cont, nu, ty (D) 8streated separately, Thus, the earlter data 1sIrealed as a l,me-
wuncated test. with T = D and the Ia!er data is lreated $eparately aher wbtracltng (D) from each observedfailure Ore.? I{ a lwODiece AMSAA model M approp,iale. Ihe system failwe rate as a funcllon of time (t) may
be e$tlmated by:
AA ;-,~llj=A, (l,/ I 0s1s/2
A
;(o=f2;21/-f2)L?-’ 1 >/2
where the parameters subscripted 1 are determined from the data prior to (D). and lhe parameterssubscripted 2 are determined from ..he data atler (D).
4.3.2.3 Illuslratitie example Th!s example illustrates how:he AM5AA model can be applied :0 apraclkal s,tualion wch aj the test of a mngle sy$; em. Ihe reliability of which is descr, bed by a Conl, nuousfunct, on. ,“ a t,me. truncated test. The IeSI data {o, thi! example are g,ven in TABLE 8 The Iesl was
lerminz led z: 100 Ghou,s Atolal of 15 fa,lures occurred at the times tnd, caleti TA3LE Balso 1,%1$SOme of
13
----- .---— __ . . . . . . ..J. -.. .z . .
---- . . . . . . . . . ------ . . . . . . . . . . . . ~
MIL-HDBK-781
I
I
the intermediate compumt, onal result% which may serve Io clarify the procedure The procedure i$a>provided in a through,
a. Ccmpute the growth parameter esumate umng equat, on 7 of TABLE 3, tha~ ,s:
h’
~=~flh’lnlo- ~ /n(X,)l= 15 f115Un 1000)-70.3121=0.4504
,=1
I b. Calculale lhe $cale.parameter estimate using equation 9 of TABLE 3, that is:
AAA = NJt~= 15/1000°”- = 0.66S2
c. Check the goodne$s Of fit of the AMSAA model at the 10 percent level of significance. Inthis case, since M = N - 1 is very close to the tabulated value for M = 15, the critical value found in TABLE 5 i$
0.169. The Cramer-von Mi%es $tat!$tic i! calculated from the observed data using equation 10 of TABLE 3,that is.
where:
~=l(.Y - 1)/ Nlfi=l(15 - lY151(0.4504) =0,42Lf4
therefore:
C; = I /l12(f5)l + 0.01857 = 0.0241
Since 0.0241 it less than 0.169, the tabulated critical value, the AMSAA model cannot be rejected If thetabulated critical values and calculated values are very close, then more exact crittical value% can be obta, nedfrom TABLE 5 by interpolation
d. %nce lhe AMSF4 model ,$ appropriate Ihe system failure rate. p(t) can be e%ttmated forlarge samples. tram:
;(f)=ffifj-le. The fa,lureraleat 1000 hour$ t%:
;(1000)= (0.6682)(0 4504) (1000 )0’--’ = 0.0067
Failure rates for other values of lime can also be computed,f. Obta#nthe lower con f,3ence bound (L~,Y)and upper con fidence bound (UN. Y) for
15 failures a“d 0.8 confidence coeff, c,enl from TABLE 7. for a t,me-terminated test. that is.
(LN,Y)= (L,5,0.8) =0.614 and(U~, Y)= U15,0.B)= 1.69. The#nterval esl, maleof MTBFlscompuled from:
/.h!.\/;(/o)s ~~Jf~= u*!. Y@”l
0614 /000675 MTllFs 1.8/0.0067
91.6 s MTliF s 268.7
14
. . . . . —------ . .. . . .. . ___ . .. .. . .. .. ---.=_e=-A. .--. —__ A_. . . ..___ A___ .__.__ - —__....-. .
MIL-HDBK-781
h. The MTBF is computed using the following equat ton:
I&tl = I /6(1000)= I /0.0067 . 149.3 hours
i. Now that the sample of 15 failures is at the margin of useabili!y of large sample
equations. As an exercise the reader should recalculate the various parameters in a through h using thesmafl sample equattons.
i. The interval est, male for failure rate can be determined from:
P“b =l/hf,A = l / 91.6=0.01 092
- 1 /Mtib - I /268.7 = 0.00372P,b -
4.4 ESS monitoring methods Three methoch for monitoring ESSare provided in 4.4.1through 4.4.3.3
44.1 Comcmted ESSlime ,nler.al method. Th!$ method provides a techmque for e$t, mallng therequired ESSUme m enwre thai, w,ih a prespecif ied high probability, all defective pans have been removedfrom a repairable system ($ee Reference 3) The required screening lime [T) for each additional system whichensures with probability (p) that no de feels remain in the sy$tem is:
()-lnp-In —
‘=+
where:
P = pre$pecif, ed Probability that no defects remain after the screening period% = exPected number of defective parts m each systemj.d = failure rate of each defect,.e pan
Furfher, let:
N< = (MP) where (Ml esIhe total number of pans in a system and (p) ,s the probabihtyIhal any one of the$e parts i! defective
Po#nt eshrcate% of (p) and (l. d) will both be bia$ed toward% making the e$timale of (T) 100 low. Therefore, it
is recommended that an upper confidence hmiton (p) and a lower confidence limit on (Ld) be used. An
uPPer (1-a) ~Onf, dence I,m,l on (P). (6) can be obtained by finding the smalle$l (p) such that:
r
MIL-HDBK-781
AI tiwer(i . ~) ~unfideme I,mit on [~). !),6), usobtained front.
x:, _,, ,,
~d.~r
21(,
i=!whew
x:, 6;:= the (1 - b)th percentile of a chi-$quare distribution with 2r degrees of freedom
,. = the operating time to the ith failure of the syslem which suffers that failure
The recommended estimate for (T), (?). becomes:
()-hp~ -h —
M~T=
‘d2
Before data becomes available to estimate (T) or (T), the screening time (T) should ~ bawd on sc,een, ng
periods for previous similar $ystems andlor engineering judgement. When and if (T) becomes smaller than:
this predetermined period, Ihe screening time should be decreased accordingly. If (T) is greater !han theQ
original period, thought should be g,ven 10 $ncreasing the screening period. A large (T) is parucularlymeamngful, of rot, r$e, II it ISbased on a relal!vely large data ba$e. that is, on a relatively large (r),
44.2 braDhi@l method In the graphical method, a plot of observed failure rate and smoothediafilure rate is made and co~l,n”ously updated from the data Typ,cally these curves will bottom out tif Ihede feclive p:,rl> are removed by E$.S The ESSdurat~on is obtained by observing when the curve becomes flat
For e~ample, In FIC,I ‘;{S 3 an ESSduration of apprommately 70 hours would be reasonable. For a new system,,
lh? lrl:[ ial ESSd... .X:,]n should be chosen from data on $#mllar syslems and then modif, ed as tesl experience,i ofcum”lal w!.
44.3 Standard ESS Standard ES5 verif, m that production workmanship, manufacturing proce%se~.
quality control procedures, and the accumulalton of de$lgn changes do not degrade the reliability wh!ch
was originally founO m be acceptable by the RQT. Th, s ESSprocedure $hould be applaed 10 all production
equipment of the system being evaluated. The equnpment should be operating when placed under the$peci lied environmental slre$~ Additional details are provided in Reference S and MI L. STD-2 164 All ,lemsshould be subject 10 a $equent!al serie$ of slres$ cycles consisting of thermal or vibration stress cycles or a
combination of both. The numbef of cycles and cycle characleri!lic~ should be selected by the procuringactivity, Typically, each equipment should be stressed until a minimum of one failure-free interval 1$
attained. The failure-free period (time or cycles) should be specified by the procuring activity. ESS can alsobe used as an effeclive screening method during development and during depot repair. After repaors havebaen completed. the screemng should be reslarled at the beginning of the next cycle.
4.4.3.1 Thermal stress A typ!cal Ihermal stress cycle ii \hown in FIGURE 4. The cycle should beselected fmm a range of temperatures between -54” C to + SSOC. The number of thermal cycles used
should range from 6 to 10. where 8 ii considered as a reasonable value for many equipments H,stoncal data
indicates that more complex equipments require more thermal cycles. Six cycles appear to be adequate for
black boxes of about 2000 pans while 10 cycles may be reqwred for equipment containing 4000 or more
parLs. A suggested range of ihermal cycles to be applted is:
C0m91exity Thermal cvclej
Simple (100 electronic parls) 1
Moderately complex (500 electronic parts) 3
16
I .
MIL-HDBK-781
Complex (2000 electron,< pans) 6Very complex (4000 electronic pans) 10
I
Hislor, cal data ,ndocates that thermal soaks do not contribute s,gnificanlly 10 the Screening effectwene$$Therefore, the dwell limes at h,gh and low temperatures need 10 be only long enough for internal
temperawre$ to Habillze. 1! follows !hat each succe~tive thermal ramp thould be \lafied won after theinternal part temperatures have stabilized within 5°C of the specified temperature and all requiredfurrcional te$u have been completed. The temperature rate of change of internal part! should fall within5°C and 20”c per minute. The best screening re$ulti will be achieved by ming the maximum safe range ofchamber mmpwatures and the greatest practicable temperature rate of change of internal parts The
equipment undergoing ESSshould be ●nergized and oparated during thermal cycling (within the $pecif tedoperaiing temperature range). but it may be turned off during chambar cool-down to permit the
temperature of inlernal pans to decline more rapidly. Equipment performance should be monitoredcontinuously, but if cost or other constraints do notpermit this, periodic chack$ and continuous monitoringof the final cycle \hould be required.
44.3.2 Vibration \tre\s, The !tandard vibration $trets $pectrum is $hown in FIGuRE S. The stress i! a
random ~ibrauon which should be applied for at least 10 minutes if the direction of vibration i$ 10 be along a$Ingle ants When vabralton along more than one axis ii required. the random vi bralion stress should be
appl!ed for a! Ieasl 5 minute~ along each axi$. The equipment should be hard-moun:ed to the shake table sothat the drrectian of wibratmn,$ perpendicular to the plane of Ihe primed circuit bo~rds (PCBS) If the
equipment ha! PCS$ oriented tn more than one plane, the ●quipment should be vibrated $equenl, ally alongeach of three orthogonal axes The tolerance for the random vibration spectrum should be .3 decibels (dB)measured in accordance w!th MIL.STO-81O, Method S14.3, Secbon 11,Tolerances paragraph Notching atresonant frequencies is permvtted
4.S MT9F assurance test The MTBF assurance lest (see Reference 6) can be used to prowde assurance
that any minimum MTBF Ie.ei. such as the lower test MTBF. ISach, eved in addil ion to provid, ng assurancethal early defect failures ha.e been eliminated The lest is conducted in combtnat, on with an E5S wh,chremoves the early defects. The procedure commences with the ES which !$ terminated after some numberof hours dettvmined by the methods prewously described. Afler the ESSis Iermlnaled, Ihe system enler$ the
MTBF assurance 1P%!,which is to be conducted under mission profile environments. The procedure ,s
destgned 10 perm,l change~ in the failure-free interval (Ie$t window) (W) if warranted by the Ieit data Thistest can be used on production equipment which has passed quallf, calion Ies:$ and can provide the producerw,th a h,gh probable, ty of wccei$. In the MTB$ assurance test, the system must operate for a $pec$f tednumber of te$t hours w!thout failure (failure-free requirement) within an interval (test window) (W) of$pec, f&ed length. Generally, Ihe test window it chosen 10 g,ve the seller a very high probabil,ly of passing the
Iesl (for ekample, 98 percent]. if the equopmenl actually doe% Jalisfy the mintmum MTBF level, Theprobability of a unit pawing, [Ps),6:
(M- 1 )’(M+ W-dPC =
~r+l
where:
,M = Minimum MTBF level, hours
w = te}t window, hours (r s W s 2r)
r = failure-free inlewal, hours
Becau\e of the large numbers invo!ved. d,recl esponenliatlon and multiplication result in numbers whichesceed the range$ol handheld calculators, therefore. lh,scalculatson must be performed i.wng logarithms,Ihal ss:
log P\=rlog(M -l)+ log(M. W-r) -(r+ l)log M
17
I
MIL-IIDBK 781
An analysis of these equat, ons nna!cated Ihat the be%kwaiue of the te%t window iV~) wa~ lvwce tne ia,l. re
If the ratio of (W) to (r) is less than two. there exists an interval within the lest durtng which one equ, pmenlfailure would immediately terminale the test in failure Thii results in degraded i(ati$tical confidence ,n the
result. Increasing the ralto of (W) to (r) beyona two, increases Ihe test time wilhoul signiiocantly ,mpro., ”gthe $lati$li <ai confidence, Therefore”, ihe Gpiim,al ratio of I=,i ‘w’fidGw length IG faiiime-free requl remen; IS2. FIGURES 6 and 7 pre$ent a graph of (Ps) versus (M) with W = 2r for a range of failure-f,ee ,IIWWEJ, of
10 hour$ to 150 hours, IJting the above equation and letting W = 2r, the failurefree interval. and,
consequently, the test window, can be computed for any desired (Ps).
For ●xampie, if P5 = C.%. ii-w equai ion yieid::
0,98 (H- l)r(Af+r).
M..1
Solving numerically for (r) in terms of (M) yield$ the ●mpirical relation:
r-o.212M
.As another example’, for an a,bilrary M = 150 hcwrl and, = 10 hw.m. the probah,li!y of arrept. ante, $f% = 0.9976.
4.S.1 Derivation of eauation, The MTBF assu(ance tesl equation is derived a%provided In a
I through g:
1 a Break up the test #nm one. hour intervals lhetefore, the ptobabihly of a wcce~% ,n any onehour interval i! approximately:
~,=c-u~ =c-l/~ e l-1/~
and the probability of failure is:
p:= l/hf
b, The Cond,lton for pas$o”g the lest m (r) hour% (, su’ce$$e$) Oi iailure-iree operalion.C. Thi$ can occur ,f (,) $IJccesses (r consecutive hours) are achiewed without tncidence of failure,
that is:
!P. )r=(l-lwf!’
d. Furthermore, the lest can be passed if following a failure, (r) successes are obtained. We are
unconcerned wtlh the prewous fa!lure htslory prmr to the Iasl fa,lure, that m:
P,(P, ) - [1/M”)(l -)/hfl-
e. Th, s czm occur (r) times with!n the WS! window (W), b.?fcwe the Ie$( is failed and 5ufflclen1
failure-free time can no I.ange, be accumulatedf, There fore(pt )(p,)r can occur (F)limes
18
MIL.HDBK-761
g. Therefore the Ioial probebiliIy of acceptance is given by:
f’s = p; + (r) (p{) @,)r
=(1- lIMS + r(llUf(l-llbf)r
-.fl-lm)’(l+rm
- (%+%)(M-I)’ (Af+r)
.Mr. M
(hf-1)’(hf+r)
~r+l
4.5.2 Procedure Using the relationships given in 4,5. the procedure provided In a through m can be
used:
a. Based on historical data wi:h !imilar ●quipment, select an ESSduration us!ng the methodsin 4.3.
b. For the desired (Pd and MT8F (0), determine the failure-free interva! from FIGUR[\ 6 and 7.c. The tes! window. W = 2r
d. Run the MTBF assurance te$l on each equipment with the parameler$ ,n a, b, and c. untilthe failure-free interval of (r) hour% ,s obtained #n the tesl window. (W),
e. Accumulate the rimes of failure on each unit (~erial number) of equipmenl tested and use
the AMSU model 10 compule current MTBF on the accumulated data and on the aata for each ,na,.tdualsystem (or some group of late~t umt>)
f. Conl, nue tesl,ng unt,l a time of 10 MTBF is accumulated.
g If the test data ind!cates a computed MTBF in the vicinity of the desired M7fl F, conl#nuetesung using the same failure.free interval and test window.
h. If the most recent data !ndicate~ a significant decrease in MTBF (reliabil,ly detertoral, on).
consider increasing the failure-free Interval and test window.i. If the most recent data Indicates a significant increase in MTBF (rehabtllty lmprovemenl),
consider decreasing the failure-free interval and lest window.
1. There is no simple method of determining, a priori, the number of latest unils who$e data
should be combined when computing the MTBF which is to be compared against :he original MTBF TheMTBF attained by each unit Iested and the overall MTBF should be calculated and graphed and the rewltt
monllored continuouslyk. If the use of a larger failure. free interval and test window results in an improvement in
MTBF, these parameters (Interval and te~: window) can eventually be reduced to the original value!
1. If the we of a smaller failure. free interval and test window re$ult$ (n a deteriorated MTBF,
these parameters (interval and tesl window) can be increased to the original value$.m This ,Ierative procedure can be repeated as the test proceeds and is e$pecia fly u$eful for
equtpment with large producllon runs.
46 Seauenl, al lest plans The sequential Iest plans are based on the assumption that the underlytn5
dlslr, but,onof l,mes.belween.f a,lure$ ,sexponential. A$et of standard PRST have found wuoeapp:,cab,lsly
19
1= ‘ , !, -- . . . . -...,..44 . . .
MIL-HDBK-781
,,, lIW Os,,,!9 :electru. ],t equ, pm.?nt ,., . bait test plan’. (l- Dthrough VI-D) are provided. The true dec, \,o -
,,sks .md d,+c. ,,, ,,nat!on rat, o! (d) for thew are:
est Plan..—
I-D 117 12.5 1.5
II-D “22.7 23.2 1.5
III-D 12 ?. 12.8 2.0IV.D 22,3 22.5 2.0
v-D 11.1 10.9 3.0VI-D 18.2 19.2 3.0
In addltio two short-ruqhigh-risk te$t plan! (VII-D and VIII-D) are provided. These test plans can be used onprograms “,1 which test time must be curtailed as a result of overriding $chedule and cost factors. The true
decision,, $ and diwiminaiion ratio$ fur these ple.m are:
lest Plan True ri$k$ Discrimination ratio—.a A g—.
VII-D 31.2 32.8 !.5
VIII. D 29.3 299 2.0
The ac. ?pt-reJect c!!leria for Ihe standard sequential lest plans are $hown graphically and in tabular form
alony w, I’*the corresponding operat, ng Characteri\Iic (OC) curves and the e,pected test time curves wh, chare bakd on assumed values of true MTBF All of lhe$e data are grouped by test plan in FIGURE5 9
Ihrot, c.. 16. A wocedure for comDutina UODe- and lower confidence Iimils cm MTBF for test~ which areterm,’ Yted by acceptance or relectnon is also provided in Reference 7. F!nclly. the Program Manager”!asm%\ <en: described on 4.6.8 provides a means to assess the effective consumer’s risk at any po, nt In ttmeI+,,! i,q a sequential test.
L.6. 1 -, The tymbols u$ed in the equations of 4.6 are:
~.
p.
g.
g, =
EJo=
r=
,0 =
To=
t.A,
1=H,
producers risk
conwmer’$ rifk
MTBF
lower test MTB F
upper test MTBF
accumulated failure$ in time (t)
failures at Iruncat, on
truncation ume
standardized acceptance time
standardized rejection time
20
Ou(Y,i) =
e~w,ll =
8U(Y,i) =
eL(?’,ll =
MIL-HDBK-731
slandardrzed upper confidence Itmits
$Iandardized lower confidmce fimili
upper confidence limit
lower confidence limit
4.6,2 Anolication. Standard PRST plans should be ●pplied when a $equential test with normal(10 percent to 20 parcent) producer’t and consumer’s risk i$ desired. Short.run. high-ri$k PRST plans may be
used when a %equential ten plan is desired, but test time is limited and both the producer and lhe consumerare willing 10 accept relatively high decition riski. PRST plans will accept material with a high MTBF or reject
material with a very low MTBF more quickly than fixed-duration test plans haw”ng similar risk~ and
discrimination ratios. Total test time may vary significantly: therefore, program co$t and schedule must beplanned to truncation. The Program Manager”% assessment in 4.6.8 providesa means 10 aswus the effective
consumer’s nsk al any point in time during a sequential test.
4,6.3 Theoretical background. The concept of $equential te$tf was developed by 1,Wald (we
Reference 8) and B. Epste, n (see Reference 9). and ii al$o di$cu$$ed by 1. Bazov$ky($ee Reference 10). For anexponential ●quipment with an unknown MT9F of (c?), the probability of failing (r) times in an accumulated
operating time (1) is:
m(:)’(y)
The sequential test must prove lhat (fl) i$ al least ●qual to or graater than the lower test MTBF [L9t) If the
true MTBF i$ exactly equal to the lower test MTBF the probability of failing (r) time$ in the Operal, ng time (I)is:
‘=1(’’=(;)’(%9In order to structure the sequential test a“ uppe, test MTBF, (O.), must also be selected, If the equ!pmenls
MTBF were equal to (8.) the probability of (r) failures in the interval (t) would be:
Now form the probability ratio:
21
MIL-HDBK-781
11,, s :auc:, ,.”, ,puted cent, nuouslydu ,ng the te$l and compared 10 Iwoprede!e, moned constants (A! and
(8). c $nq the ,!c?cts+on rules ofa through c’
:. lf P(r) becomes < B, accept and stop Iesl, ng1. If P(r) becomes > A, reject and stop Iesllng
if B < P(r) < A, continue testing
The conslaf,l$ 1+1 and (B) are:
(1–~)(d+l)A=
2ad
PB=—
(1 -a)
where.
n ,. pr~ucer’s risk
P= consumer’s risk
d= discritni”alionralio
The graphical sequential test procedure i~ derived a$ follows:
Thelerm for [A)contatns thecorrection factor(l + d)/2dwhich, \foundin Reference9. This fac!or
wbslant, ally reduces the differences between actual and achieved consumer’s and producer’s ri<ks wh, charise because of Iesttruocat, on Theorog, nalsequenl, al Iestderi vations donotaccount fortheeffecloftruncation On the r,~k!
Starting with
+7” ‘l’ml’-’lfill<A<A1
Take the natural Iogartthms
h/J< rln(Oo/8 ,1+(1/0 - llO,lICh Au
Transform this inequality bydividing alllerm$ byln(g~el)a tieradding( l/@l-l/80)tt oeachlerm. Thl~
results in:
in B (1/0, – I/eo) lnA (1/0, - 1/9.)—+ (<, < —+ iin (O./O, ) In (O./O, ) 1. (0/31) ln(OdOl)
As long as the numerical value of (r) !s between the values of the left and right side of the inequality. the lestcontinues. If (r] becomes equal toorless than theleh5ide, thetest lerm, natesin anacceptdeci%lon When
(r) becomes equal loorgreater lhanthe right $ide.lhe testterm!nales inarejectdect$ion. Theexprewons
on both wde%of the, neaual,ly areeq.at, onsof twoparallel stralght:lnes: lhus, theinequallty can bewritlen as:
a. bt<r<c+bt
22
MIL-tiDBK-781
II
When these two Iinesare plotted on graph paper with(l) (cumulative lest I,me) as the ab$c, ssa and (r)(number of fa!lurei) ai the oral, na:e,lhe constants (a and c) are the $ntercept$ of lhese I$nes w,th the ordlnale
and (b) i~the dope
The numerical computation o{ a, c. and b is given by:
1“ M~=—
;“ (oo,a , ;
h A~=—In (@#l)
(1/0, - 1/6.)b=—
/n(oJe, )
From this. the two parallel lines can be plotted on graph paper in an (r - 1) coordinate system. By draw~ng a
Mmzontal lane at (r = ro) and a .enical line at (1 = Toj, the lesl is Iruncaleo
4.6.4 lest truncation The sequential tests provided in th!s handbook are all truncated ie$ts becau$eof the pracucal requirements of real-world test programs. The method for truncating a sequential test was
developed in the paper written by B Epstein and M. Sobel ($ee Reference 9).
The ~PP,oPriate VaIUe of (,) ii the smallest integer that can be used $0 that:
x:,. ”,,,, 8,—Zc
x; ~, o
where X:, - .), ~,, and X~, ~, are the cht-square variables with (2r) degrees of freedom Table$ Of lhe chi.
square distributmn can be found tn Reference 11. The$e IWO values are found by stmultaneou$ly $earchmgIhe (1 a ) and @probabiltl, es of Ihe civ.square tabies unlil the Ialio oi the varlabies is equai 10, or greater
than, @,/L?o When this poinl, %found, the degrees of freedom are set equal 10 (2r) The value Of fr), %alwaYSrounded to the next highest integer
Th,~ .aI”e is (rO). From Ibis, the max,mum time (To) can be found
oox2#, _u,,=‘f” =
0
2
4.6.5 Seauemial te!t example. A PRST plan maybe generated analytically for any given (a). (~),
( (1)), and ( 6’o). The procedure M $lra*ght fo~ard and can be ea$ify implemented with a hand-heldcalculator. For example, given the following input data:
~= 0.10
p = 0.10
0. 100 hours1
Delermtne the dtscriminatoon rauo, accept. reject criteria, truncation po!nts, and the dope and oral, natennterceotso’ the lest plan curves PIOI the test plan. The solution proceeds af spec, f#ed (n a through e:
23
.-. . . .. .. _.,_
MI1.-HDBK-7B1
oa. Discrimination ratio = d=:=~=2
1
b.(d+l)( l-p) (2+1)(1-0.10)=675
A=2aIf ‘--2(2)(0.10) “ ‘
c. PB=~
0.10=—.-.0.111
-a l-o .10
cf. Compute the points of truncation as follows: Search the chi-square tables at the upperconfidence (1 - a ) and @) upper percentage pointf until a point if reached at which:
or,
X:,,,r— 20.5X20.1:2,
This point occurs at 29 degree$ of freedom where:
X:9,2, 19.763 “— - — -0.506
x:,, ,2, 39.087
therefore:
2r = 29
r = 14.5
10 = 15 foilurea
and since:
eox2, )_o,.2,To=
2
200 (20.61To=—
2
7’0 = 2060 hours
The test, therefore, should not last longer than 15 failures. or 2060 hours,
e. Determine the dope and oral, nate intercepts of the two parallel straight lines:
1. B In 0.111 -2.198~=— .— .
fll(oo/o,l—=-3.17
in 2 0.693
24
l___ . . . . . . . . . . . . . ..+z-e.-. =- e.-..==-=--- .--, ~-.. - .-—-—-- .-.x -_-—. .“ -----
MIL-HDBK-781
I
(1/0, - 1/0,,1 (0.01 - 0.005)h=
Ill Wolu,l == 0.00721
In 2
In A In 6.75 1.910— - 2.75
C= —= —-0.693/n(OJell t. 2
These values are plotted in FIGURE 8. .
4,6.6 Standard PRST acceol-reiect criteria and OC curves. FIGuRES 9 through 16 presenl the accept.reject crileria for the Standard PI?STplanf and the OC and Expected Te$t Time (EtT) curves for Test Plans I-Dthrough VIII-D. The OC curves plot values of probability of acceptance verws the true MTBF expressed inmultiples of (@l) and (80). The ET? curve plos values of expected test lime ver$us time MTBF ●xpre$$ed inmultiples of (e, ) and (80).
4.67 Confidence I,mm for wauential tests This me;hod for e$limating confidence limits can be used
w ●stimate the con{tdence I,mit% on MT8F at the completion of the sequential tests described on Tesx PlansI-D through VIII. D. Table$ of confidence I#mits on the true MTBF are given in TABLES 9A and 90 and 10A
and 10B Acceptance can occur only aI discrete limes. while relection can occur at any tome after therequ~red number of fa,lures has occurred Therefore, confidence limit% aher acceptance and rejecuon mustbe computed separately. TABLES 9A and 9B present confidence limits al acceptance and TABLES 10A and108 present confidence Itm, ts at reiect#on. Def!ne (tA,) as the Ha”dard,zed acceptance time. so that an
equipment 15accepted if not more than (i) failurei occur in (lA, ,) hours. Def, ne (lR,) as the Nafldardtzedre)erc, on tome, so that equtpment ISrejected if al least (i) failure, occur at or before (tR, ,) hour% Together.
(tat) and (tR,) are the standardized termlnat,on tnmes The actual termination times are obtained bymultiplying the standardized term! nat, on Itmes by ,. The standardized lower test MTBF is a$wmed to
equal 1,
46.7.1 Confidence Itmdts a: acceptance. TABLE 9A presents conservative [1 - Y) 100 percent
standardized lower con f,aence I,mm (19[(7.1)) and [ 1 -Y) 100 percent standardized uPPer confidence Ilmit$
(8~(Y.i)) on the MTBF for all tests lerm,nated by an accept decision wing Test Plans 1.0 through VIII.D forY = .5. .3, .2. .1, .05. A comervauve Ibvo-s,ded (1 - 2Y) 100 percent standardized confidence ,nter.al, %
@L( Y,i). c?~(Y,i) Aclual limits and !n:erval! are obla,ned by mult!plylng (e~(Y,i)) and (@~(Y,!)) by the lowerIeit M.TBF (t?,) That ,$:
O,~(Y,iJ =(fl Oj(Y,i)
O; (Y. I1=U1lf~ (_Y,i)
4.67.1.1 Examole black boa X The follo~g e,ampleisba%edona production reliability
acceptance teit of a black boh X for an a,rcraft. The example can be stated as follows:
The Government agrees to accepl a monthly production lot of 40 units wl!h probability 1 - a = 0.8, if the
\rue MTBF f70 . 100 hours and will reject the lot with probability 1 - /3 = 0.8, if ;he true MTBf 8, . SO
hours The designated ,I!ks are thu$ a = @ = 0.2, and the discrimination ratio (d) = 100I5O = 2.
Consequently. Test Plan IV-D must be used. The required minimum sample size is three unitj FromFIGuRE 12, the lot is accepted wilh O fadure! after 1*o g?, = 2.8x 50 hours = 140hours, or wilh I failure afler
IA18. . 4.18 x50hours = 209 hours. and so on, vnce L*O = 2.8, tAj = 4.18, and so forth, are the
Standardized acceptance t#mes Assume on the aclual test that relevanl fatlure$ occurred al 50 hours,90 hours, 120 hours, 250 hours. and 390 hours of accumulated test t#me The accePt and rejecl Itme% al eachof the fa:lure$determ!ned from FIGuq E 12area$follow$:
25
MI1.-HDBK-781
Number of failure> Reiecl lame Acceot ttme Actual tome
o 2.80X 50 = 1401 4.18x50 = 209 501 0.7 Xso = 35 5.58 X 50 = 279 903 2.08150 = 104 6.96 X 50 = 348 120
4 3.46x 50 = 173 a.34x50 = 4\7 25o
5 4.86 .5.0 = 243 9.74 I 50 = 4a7 390
This data indicates that the tolal accumulated lime$ al 1.2, 3, 4. and 5 failures do not lead 10 rejection, and
the lot is accepted with 5 Iailwej after 9.74 x 50 hours = 4B? hours total lest time (IA = 9.74, thereforeTA = 9.74 x @I) Suppose that an 80 percent lower confidence I!mit on the MTBF is denred. First I,nd the
conservative BO percent %Iandard!zed lower confidence Ilmit l?[(~. ,) = 8[ (0.2,5) = 1.0459 from the
aPPrOPrlale entry fOr Test plan IV-D on TABLE 9A for Y = 0.2 and 5 failure!. A conservative 80 percenl lowerconfidence I!miton the !MTBF ,s ;.01159 R $, or 1.0459 x 50 = 52.3 hours Similarly, aconservat, ve80perc e..!
upper confidence llmll On the MTBF from TABLE 9B is I%(Y. i) x& = 2.5225x 50 = 126.1 hour%.where 8~(0.2 .5) = 2.5225 comet from TABLE 9B for 7 = 0.2. i = 5.
4.6.7.2 Confidence limit~at re!ect, on TABLES 10Aand 10B present exact (1 -Y) 100 percent
standardized lower confidence l,mrti (8:(7.0) and (1 -Y) 100percen~ standardized upper confidence I, T.I<,%
(L%(Y,l)I on the M?BC for Te$: plans I-D through VIII-D te~ina:ed by .i r~!ect dec,$,on for selected values o!lhe standardized I,me (t) and 7= .5, .3. .2, ,1, .05. Atesl maybe terminated bya relectdec, socm atanyt, ms
(t), once a reqw, ed number of fa,lures has occurred. Therefore. it i!impo!sible Iolabulal econftdence ltm,:~for all possible outcomes Use I,near tnterpo:al,on for nontab”lated values of $landard,zed (t)whwe (t)
equals the actual total te~t t)me (T) dtwded by the lower le$l MTBF (f%), or in }pecial ca$e$, u$e [he X‘d,%trlbullon for exac! I:m,l% Consider the ca$e where re]ecuon of eqwpment occurs af!er(t(%) hours of total test I,me. If (t) exceeds [he smallest value in TABLE IOA, the(l - 7] 100percent lowerconfidence I,mil can be calculated as$pecif, ed #n athrcwgh c
a From TABLE 10Aobta, ” (L?3[(Y,t, )] and (0:(7,17)) wchthal (t, } < I < (t2) and {1. ) ,* (he
largest table time Ie,i than I and {t2) i} the!mallest Iablel, megreale, lhan I
b By%:mple ,merpolatto!? I!nd:
e;l Y./l - 0;. (Y,/,) + (!3; (7,(.) - 0;. (Y.l,l)(f - l, L//2_l
c. The actual (1 - Y) 100percent lower confidence limit onlhe MTBF based ona rejecl!on
aher (t e,) hours then
OL(Y,II =olo; (Y,f)
If (1) is smaller than the smallest value ,“ TABLE 10A use the relatiomhip between the X’ and the Pcmson
distnbultons 10 CalCulate Ihe [1 - Y ) 100 percent slandardtzed lower confidence I,mit on the MTBF asfollow~:
I-IL (y./l . 2f/x2 ).?.2,
where X (I ~,1, ,sthe (1 .7) 100th percenlileo! the X’d,stribul,On with (2i) degrees of freedom, and (!) o%the number of fa!lure$ wh, ch lead tore, ect, on a! t,me [: 8,)
26
MIL-HDBK-781
Then:
e’ IY,f) = e, e; (Y,t)
Similady calculate a (1 - Y ) lDD percent mzmdardized upper confidence limit [ 8L(Y.W on MTBf by
interpolation if (t) exceeds the smallt$i value in TABLE 10B.
If t is smaller than the $mallest value in TABLE 10B, use:
e“ (Y,fl =21/x: *,
where Xj,2, is the Y 100th percentile of lhe X’distribution with (2i) degree$ of freedom. A (1 - 27) 100percent confidence interval on the MTBF for a test terminated by rejeclion aher (II%) hours is
<e, eL(Y, L),e,eu(Y,l)>
4.6,7.2.1 ExamDle: black boz X Suppo$e that in the previous example failures occurred afterSOhours, 90 hours, 120 hours, and 1S0 hours tolal teal lime
The accept and reject umes at each of the failures are determined from FIGURE 12 as follow$:
Number of failure% Reiect time Accept time Actual t,me
o 2.80 x 50 = 140
1 4.18150 = 209 50
2 0.7150 = 35 5.58x 50 = 279 90
3 2.08XS0 = 104 6.96 x 50 = 348 120
d 3.46x sO = 173 8.34x5O = 417 150
From these tabu:ated .a!ues it can be $een that Test Plan IV. Ddoes nol require rejection after 1, 2, or 3
failures. nor acceptance before 150 hours. However, the lot is ,ejected after the fourth failure (that 8s, 150hours) since it occur% before tRa .8, . 3.46x 50 = 173 hours. The value tRt, = 3.46 is taken from FIGURE 12.
An 80 percent lower confidence I,mit on the MTBF 15calculated as $pecifoed in a and b:
a, Fir\t find 8{(Y.tl= t): (0.2,3) wheret = T/81 = 1S0/50 = 3. lnTA8LE 10A. t, = 2.80with 8;( 0.2, 2.8) = 0.5646 and t2 . 3.46 with 8[ (0.2. 3.46) = 0.6644. Using Ihe equation in 4.6.7.2 b,calculate o: (0.2. 3) = 0.595 by interpolation. An 80 percent lower con fidence,limil on the MTBF g#ven arelecttonatmr 3 xe~ = 150hours,s I?[(o.2. 3) x et = 0.595 x 50 = 29.7 hours
b. Similarly, calculate an 80 percenl upper confidence Ilmll. From TABLE 10B obla, nLJL(O.2. 2.8) = 1.5517 and t9(J(0.2. 3.46) = 1.7379, giving @~(O.2, 3) = 1.608. An upper Confidence hmtl onthe MTBF gtven a rejecuon after 1SOhourss% @~(O.2, 3) x 8, = 1.608 a SO = 80.4 hOur$
4.6.8 ~t. The Program Manager’s assessment providesa means for toe Government to as$eis the ccmwmer’s risk at any po, nt in t,me during a sequential tesl Th!$IS especially tmporwml in case% where Drogram time and schedule pressures may force the Program Manager
Io consider an early Ierminalionof the test
1 .. ----....
27
MIL-HDBK-781
4.6.t. Pro\edure The Program Mmdgur’s asies%mea,, tan be implemented using the procedure%peclfied ic . :hrough d
a. Al ihe point where the lest is halted, compute the probability ratio:
.UIIO, I-l UUOIILp (r) - (kfJkj)’ c
tirre.
80. upper w$l MTBF
r = number of failurm
f = te$t hall time
b. Setp(r)=(l -f3)/a
13 = consumer”% rifk
Q = producer’s risk
c. Compute the new value of /3 = f3( Irom the equat,on ,n step b at the same ( a ) levelcf. B’ Isaneffec:!ve con%umer’s risk al anytime,(t)
Th!s procedure should be used exduswely by [he Program Manager. If the test appears to be heading
towards an early reject. the Program Manager should not allow me lest 10 be halted. If the test appears 10
be t,eading toward$ an early acceptance the Program Manager may permil an early acceptance if the valueof <onsumer’$ risk is not seriously increased. The final decis, on can only be made after the COSISof add{ t#onal
testing are we, ghed against the ,ncrea5ed nsk$ of ●arly acceptance.
4.7 Fixed-d ”ration test! Fixed-duration tesl$ offer a distinct advantage for program planning,
namely, prior knowledge of test duration wh,ch perm, ts program planners to perform wade-off !tudies
between test duration, consumer’s and producer’s rash, ( 190) and ( O,). See the discussion in Reference 10
4.7.1 m. The following $ymbol$ are used on the ●quation% defining lowed-duration test plan$
discussed in4.7:
T = test termination lime
k = number of failure!
a = accept number
r = reject number
c = confidence
TI = accept time if (j) failures have occurred to that tome
28
MIL-HDBK-7B1
!
I
Four cliff.?, en: ca:egor, e%ol I,seo.durat, on Iesl$ must be considered dependnng onwhelher the test ,s time
Ierm, nated or fa,lure lerm, nated. and whether the test ,s conducted with or withoul replacement of faileduml% In the case of I,xed. duration, twne-lermin alea tests conducted vwlh replacement, the Ie, minal!on
tome, (T), and the accepl (a) and reJect (r) numbers, can be determined from two equations:
rrio, te-”r%I–II.
<
,.. +1 k!
(TIOO) be- ‘rnO~-: f
h=.&!
The right.hand expression of each equation is ah upper tail cumulative Poiswn whkh can be evaluated with
appropriate table$ (see Reference 10) of with same programmable pocket calculators. Some Poisson tablesprovide only the lower lail cumulative termi. in which ca$a the equatiom may be rewritten as:
(TIO,)ke-rm I
0=s,.”
&!
CZ! (T/Ool&e-TfiO
l–o=}
A.(Ik!
Note that ihe accepl (a) number is relaied to the reject (r) number by a = r - I !0 ensure that the te~ireaches a dec, s,on on the allotted lest time. Th!f relation!hrp between (a) and (r) means thal the $Olut,on oflhe pair of de fin, ng equal, ons used must be oblained by an nteralive process. The mtmmum pom,ble test
ome can be found In lhe accept equauon by wbstituting a = Oand the appropriate values for 8 and 0;.However, lh, s value of (T) subsl, tu:ed ,n the ,eject equalian, together with d, and r = !. w,II normally y,efd
a value of ( a ) which 1$100 large, indicating that (T) i~ 100 small. The value of (a) i$ increased by 1, againsolwng for (TJ Tms value of (T) and the new r = a + 1 are Ihen substituted in the equal, on for ( a): lh, sprocess #srepealed until Ihe value of(o) i$ less Iha”, o, equal to, the required ( o). The values o+ (T, a. and r)
tin th!i ftnaf calcuiat, on conscitu[e the ciecis;on rule for the desired plan.
47.2 Eaamule moblem Amnnelhala plan with a = @ = 0.2 and d = 2 is required Iotesl for
k, = 50(1 hours. Using the cumulative Poisson table in Reference 11 to solve the equauon for 1 - /3 w,tha = 0.(1 - 6) = 0.80, and 81 = 500, a value of l,600r800houn isoblained. Subst, tul, ng T = 800. r = 1,and (76 = 1000 an the equauon for ( a ) yoelds a = 0.55. S,We m,s is tao Ia,ge, a M imreased to 1 (or which T os
3.0 t?, or lSOOhours Uwng T = 1500 hour$. r = I,and 8.= 1000, ntheequalmn for( a) resulls,n o= 0.4L,wh$cn is still 100 large, Continuing this process. it ,S I,nally determined thal a = 5, r = 6. and T = 7.88,, or
3900 hours Thi$ w,ll produce an a= 0.2$01 hat the tesl dec,mon rule isl = 3900. a = 5, r = 6, or leslfor3900 hours: accept if 5 or less failures a,e observed. and reject cl 6 or more failure$ are observed (seeFIGuRE 17)
4.7.3 Slandard fized.duraf, on cestolans and C2Ccurve$ Twelve oilhemosl frequently u%edor
standard TeslPlans lX-D1o XVll-Dand Xl X- D1o XXl-Dare summac&zed{n TABLES 11 and 12, fespecltvefyThese plans provide aconsiderabl era"geof alternatives forle$t co"slruclion. Theco,respondtng OCcurve$
areshown in FlGURES23t034. The Po, ssonformula lo, compiling theOCcurves is repeated below:
where
p(e) = PrODab#ltty O!accepl, ng,lems w,ll)an M?BFo! O
29
MIL-HDBK-781
r = cr, i,cal (re, ect) numner of Iallures
T = test term! natton Ijme
The quantity (r) i~ determined so that:
P(eo) = 1 –a and/P(O,) 2 p
LJ.4 Alwrnative fixed.duratio~ lest fian$. The alternative plans provide a comprehensive $el offixed-duration plans for 10 percent. 20percenL and 30 percent consumer’% risk (19), covering a wide range of
test limes. These plans are presemed in FIGURES 18 through 20
4.7.4. I Derivation of alternal#ve olans. In order to derive a fixed-duration lest plan from thesefigures, cho~e the COnWmer’S ,isk (J3) a“d turn to the appropriate figure (FIGURE 18 for 10 perCenl
conwmer’j risk, for example). Based on the tesl ume available, *elect the ten crilerla which besi apply 10 thesituation. For example, a test plan with a consumer’s risk of 10 percent and a !otal test time not to eaceed
9.3 multiples of the lower test MTBF ISdesired In FIGURE 18. under column head,ng the TOTAL TEST TIME(T) (multiple$ of f7, ), ftnd the lest time doses! 109.3 which does not exceed it In this case. the tesl lime
would be 9.27 muluplesof ( s9,), Read, ng across therowcorrespond, ng 109.27. the test plan number IS 10-6
This test plan will accepl equipmenl if 5 or Ie$$ failures occur during lhe 927 K 8, hours of Iesung 11W,! Irejec! lhe equipment if 6 or more failures occur during that period The row alio defines the worst case
(accept with 5 failures) acceptable observed MTBF (d), whtch for Test Plan 10-6 i> 1.55 multiples of [ .9.,)The d,scriminat, on ,atIos corresponding 10 producer’s rnsk%of 10 percent, 20 percent. and 30 percent are
prowded in the last three columns Aga, n, ,n Ihe case of Test Plan 10.6 for a producer’s risk of 30 percert.the d,scnmination rauo ,s 2.05:1. Stm!iarly, fora pmducer’sn%k of 10percenl, lhe d,scriminauon ratto IS1.94:1. The procuring acuvaly should select test Plan$ from these table> If It is felt that such a lest Plan 8smore appropriate than the standard plan$
4.7.5 MTBF e%umation from observed test data When the procurong activity musl have a Slal, sucalba$i! for delermoning contractual comp!nance, and a basi$ for esl, matmg the f,eld service MTBF values, aftxed-duratoon test plan must be wed. Whele requ, red. all agencies conducting reliability tests under theprovisions of this handbooL should provide the procuring activity with current values of demonstrated MT8f
(~) m each required te$t repofl
47.6 Exclus, on of hvpothe~, s test values Since they are assumptions rather than test results. ne, ther
the upper te%t MTBF ( 8.) nor the lower test MTBI ( cT!) 01 any test plan can be used m ●slbmale
demonstra~ed MTBF The demonstrated MTBF (8) must be calculated from demonstrated test resultsProducer’s ri!k (a) and con$umer’~ rmk (~) are excluded from the!e Calculations since they refer to the
probability of passing or failing the test rather than to the probable range of true MTBF demon$Irated
during the test. However. the tesl parameter value$ ( f?0,81, a. /3 ) should be provided
4.7.7 Soecif,ed confidence interval In order 10 obtain an ,nlerval estimate of the demonstratedMTBF, the procurang activity must $pec, fy the confidence interval. The confidence interval is ●qual to(100 - ~j percent. For example, given g equals 10 percent. the confidence interval ●quak 1OO[2)(10), which
●qual$ 80 percent.
4.7.8 MTBF estimation from ftxed.duralion test plans. When a fined-duration test plan i$ specif, ed.
an interval estimate of the demomcrated MTBF of the te~t sample can be estimated within the ~pecif ledconfidence tmerval, When a test report is due, the aclivily conducting the test should estimate the MTilF
and confidence interval using lhe procedures specified In 4.7.8. I thlough 4.7.8.2.1.
A.7. B 1 MTBF esltm ation al failure occurrence This estimation can be made when a lesl iS In PrOcess
or has terminated !n a reject decnsmn The procedure ISas spec$f, ed In a Ihrough e.
30
,. —.—
MIL-HDBK-781
,a. calculate the observed MTB~ (6’) by d~vidiw the ma! operating lime of the eWIPment
at the occurrence of the most recent chargeable failure bylhe number of chargeable faolures
b. Enter TABLE 13 or FIGURE 21 with tOtal failures and lhe $pecified cOnfhdence inlerval.Read the lower and upper conl,dence mulliplter for that number of failuce$.
c. Mull! ply observed MTBF (4) calculated by step a by both the upper and lower confidencelimit mu!hpliers to obtain Ihe lower and upper demonstrated MTBF ualu-.
d. Record demonstrated MTB~as the $pecified percentage of confidence, followed by thelower and upper MTBF value$ in parenthesis: @= XX percent (lower hmit MTBF, upper limit MTBF). MTBF
values should be rounded off to the nearest whole number.
e. If the Malue$ are nol available in TABLE 13 or FIGURE 21, then the correct value$ can beobtained by computation as follow%
MTBF multiplier = 2r lower limits
X;I..V2; Z
where:
. 2r upper limit}
X:, +=m, %
r= number of failures
X2= chi-square distribution
c= con fidence interval (percent pe,100)
4.7.8 .1.1 Examcde al failure occurrence. Thespecified con fidence inlerval is80percent; therefore(1 + c)12 = 0.9and(l-c)/2 = 0.1. Theseventh failure occurs at820hours tolalle%t time. Therefore,observed MTBF(~)is 117.14 hour$. Enter TABLE 13(or FlGURE21) with $evenfailures andthe90 percent
uPperand lower limit$and find thelower limit mu ftiplier of 0.665and anupper lum'tmultlpl'erof 1.797.The product of these multipliers with the observed MTBF yield% a lower limit MTBF of 77.9 hours and an
upper limit MTBFof 210.5 hours There isan80percent pfobabilily lhalthe true MTB$will be bounded bythis internal. There i$alsoa 90percenl probability !hallhe true MT8Fofthe $ampleequipment iiequal to orgreater than 77.9 hours, and a 90 percent probability that iti$ ●qu@ to or Ie!s than 210.5 hours
Demon! lrated MTBFalthis poinIin thete!: will berepofleda$: 8= BOpercenl (7 B/211 )h0ur$:
4.7. B.2 MTBFe$limation alacceotance. The calculation ofalhrough eshould bemadewhenthe
tes: is terminated in an accept decision.
a. Calculale theobserved MTBF(4) bydiuiding thetotal operating time oflhe equipmentby the number of chargeable failurei
b. Enter TAB LE140r FlGURE21 wilhtotal failure$ andthesPecifled confidence interval.Read outthelower andupper con ftdencemul ,pliers forlhat number of failvre$.
dc. Multiply ob$erved?JTBF( )(calculaWcfin a) by boththeup perandlo werconfidencemultipliers to obtain the lower and upper demonstrated MTBF value~.
d. Record demonstrated MTB~asthe s~cified ~rcentage ofconf,dence followed by thelower andupper MTBFvalues lnparenthesi$: c9= XXpercent (lower limil MTBf. upper limil MTBF) MTBF
values will be rounded off to the nearest whole number.
e. lftheval ueiarenol available in TABLE 140r FlGURE 21. then ~hecorrecl values can be
31
. .—
MIL-HDBK-7f31
.. ... rwd by compulauon M Iollo’w
MTBF multiplier = 2r lower Iimat$
x:, -,,n.2r+2
. 2r upper limits
X;,,c)n. z...he, e.
r = number of failures
X2 = chi+quare distribul,on
c = confidence interva! (percent per100)
4.7.8.2.1 Example al acceptance The specif,ed confidence Interval IS80 percent. The test reached
an accept decuslon after 920 hour% of Iesl, ng w!th seven failures occurring during that period. Therefore, lheobserved MTBF (d) IS 131 hours Enter TABLE 14 w,lh seven failures and lhe 90 percent upper and lowerIimitsand ftind the a lower Itm,t mulllpl,er o 0,595 and an upper Iimlt mulllplterof 1.797. The produclof
dthese mullipl!ers wl[hlhe observed MTBF ( ) y,eldsa lower lrmil MTBF of 78.2 hours and an upper Itm, th.~T8F of 236 hours. There ,s an 80 percent probability !Iml the true MTBF is bounded by this inlerval There~l~o ,%a 90 percent probab,l, !y that true MTBF of the sample equipment ;$ equaf to or greater lhan 78 hours,
and a 90 percenl probab,l, ty thal at ,s equal 100, Ie!\ than 236 hours The demonstrated MTBF at the end of
the [est WIII be reported as 1?= 80 percent (78/236) hours
47.9 Proiecl, on of exgected fteld MTBF The contractor (or tesl agency, if other than the contractor)should be responsible Ior prowdong demonstrated MTBF under test Conditions. The procurtng activityshould be responsible for pvolectlng expected MTBF under I,eld service conditions. This re~ponsibil, [y can bedelegated to the contractor (or test acvwty. C{other than the contractor ) when so specified in the conlracl
47.10 $ixed.duration test!: Prooram Manaaer’$ assessment. The standard fixed-duration test plar.~are characterized by Ihelr dtiscrfim, nal, on ralio (d), Ioial test I$me (T). and maximum allowable number of
failures m accept (k), If a fixed-duralmn Ie%l plan ,s selected, the total test duration is set in advance The
only way these plans can terminate early i! by reject!on For e~ample, Tesl Plan XVII-D lerm#nates wtlh areject dec, uon al the th, rd {allur e,{ th!s failure occurs before 4.3 umt$of total lest lime An accept dec, s,oncan only be made when 4,3 un, t$ of total te$t tame ha.e been completed. Even if the second failure occdrsvery .?arly, anearly reject dec, s,on cannot be made; no, canan early accept deci, ion be made if no failureshave occurred, for example, by 4.0 units of total test tame In both 01 these wlualions, an early decisionwould lack !Iatl$ tical val, d,ly by falllng 10 guaranlee the OC of (he selected plan Also, an early reject
decision by the consumer would probably v,olale conwaclual agreements wllh the producer. However, an
early accept decismn by Ihe consumer would not be wblecl 10 such an objeclion Such a dec!sion might
aPPear to be very desirable 10 the conwm~ (Government if test costs were high or if schedule deadllne$were approaching. Modifications 10 the standard f!xed-dural!on le$l plans which allow early accept
deciwom 10 be made w,thout sacrificing staust,ca! validity ($ee Reference 12) are provided in 4.7.10.1through 4.7.10.3. The proposed plans differ from the probabtlily ratio sequential te$t$ in this handbook inthat rejection i! permitted only a her a fixed number of failures have been observed.
4.7.10 1 AcceP1 times The accepl ttmes [TJI of !he Program Managerti assessment are tabulated anTABLE 15 in mu ftiple$of(el) ACCepIZWe Occur, ,f “01 more than ~) failures have occurred 10 Itat lame
4.7.10.2 Comrlanson w,th standard fixed -dural, on tes!% TABLE 161nd, cate% how the consxmec<s
and producer’s ri$h$ are modtf ted by the Program Manager”s assessment foaed.durahon lest% TABLE 17
comoares the max, mum test ttmes and number O{ Ia#lurestorejec!
MIL-HDBK-781
I
I
4.7. 10.3 OC curves. flGURES 22 through 34prov@ecurve$of expected Iesl duration versus lrue
MTff F for the Program Manager’s asses$menl f#xed.duraliOn Iew$.
4.8 A1l-Eccui Dmenl Production Reliability Accemance Test Plan. The basic Ail. Equipment Prod uctmnReliability Acceptance Test Plan (Te!t Plan XVIII-D) should be used when all units of produclton equipment
(or preproduction equipment, if required by the procuring activity) must undergo a reliability 101acceptancetest The plan deplcled on FIGuRE 35 includes a rejecl line and a boundary line. Both line% may ●xtend as far
as necessary to cover the total t?it ttme required for the production run. The reject and boundary Ilneequations are the same respectively a$ !hme for the reject and accept lines of Sequential Test Plan III-D The
equation of the reject line is f~ = 0.721 + 2.50 where (T) i$ cumulative lest time in multiples of ( # I), and (f)is the cumulative number of failure$. The plotting ordinate is for failure~ and the abcciwa is for multiples of
( @I). the lower lest MTSF. The boundary line if 5.67 faiiure~ below and parallel to the reject line. Theequation is fB = 0.72T - 3.17. flGURE 36 present$lhe OC curves.
4.8.1 Test duration. The test duration for ●ach equipment should be specified in the lesl procedure
and approved by The procurong acliwly. Unless olherwme specifoed by the procuring acli.ily. the maximumdurdlton should be SOhours and the minimum duration should be >0 hour% where time i~ co. ntec! m the
next h,gher integral number of complete test cycles Ifa failure occurs in the Ia$t test cycle, the un, t Snou!dbe cepa, red and another cc,mplete test cycle run to verify the repair.
4.8,2 Evaluation., When Test Plan XVIII-D is used, all production units should be wbjecled 10 the
env::onmcmial teji :aw!; tiims in :Re ap~:o;e~ :e:i p:o:edure. Ctmwlative equipmen: oper3:ing h.me and
equ, pmenl faiiure~ should be recorded, plotted on the chart of the lesl plan, and evaluated in accordancewtth the cricer#a of flGURE 35 and 4.8.3 through 4.8.3.3.
6.83 AcceD1. rejecl criteria for the all.equiDmenl test Accepl. reject criteria for the all-e.q ,!pmenl
tesl is slated in 4.8.3.1 inrough C.g.5 .3.
483.1 Acceolance If the specified lest ume is completed without reaching the rejecl Ifne, all of the
eqmpment which the lot under test compri$esare considered 10 be acceptable, provided thal eachequipment conforms to the $pecif!ed normal performance acceptance test criteria.
4.8.3.2 Re[eclion If a plot of failwe5-verws. time reaches or crosses the reject lane. the eqwpmenl101under lest ,s no longer acceptable. The test should then be termi”aled and corrective action undertaken
4.83.3 Reach, nq the boundary line. If the DIOI of failwes-venus.time cro$ses below the boundary
line and lhe next fa,lure point i~ al Iea$t one failure interval below the boundary lone. the PIO1 should be
brought verctcal{y up w Ihe boundary hne. If the failure point is less than one failure interva! below theboundary Isne, the plot should be brought vertically up one failure interval, cro$sing the boundary Itne Thisis eqwvalent 10 censoring lest time as necessary at each failure in order m maintain a failure PIO1 w,lhoul
1.-.8~ill “CII r~pr~senltrueaccumulated test I,me AllCrosi!ng the boundary line. ?here!ore, !h? !?s1 !ime p-.lesl t,me should be recorded in the test tog to maintain the capability 10 determine lrve accumulated te$llime An accurate or true plot of accumulated test time and Iailwes$hould be maintained cm the same thanby cent, nuting the PIOC into the regoon beyond the boundary line. In order to mainta, n the proper rejectcrileria, the f#rsl failure occurring after the boundary line M crossed should be shihed vertically 10 thebounclary I,r,.s 10 star, a seccir,ci FJlti, [d~iid lir,e) wiik,ir, i$,~ ~cce~, and cc.r, tinue tes: region, i! fa!lwe$ occdr
oflen enough. If anolher fa#lure does not occur for an extended period of time. there would be no secondplol and the or#ginal true plot should be continued. The next failure should be plotted on the boundary lone
d,rectly above the Ciue plolled point (failure 7 of FIGuRE 36). When several failures occur in rapidwccewon. the second PIO1 (dolled I#ne w,th fa!lures vemcally spaced al exacl $ingle failure intervals] would
reach the re, ecc lane, and lesl, ng would be terminated and correcli.e acl, on undertaken Aller the
approved COrrec live act, On ,s completed. Che testing should be resumed and the true plot conl, nued Thecumulative number of failurei and lime shown by the true plot would bereadd; reclly from Ihe {allure andI,me icale} The fa,lure$ plotted on or above the bo’undary Ihne after the t$me plot crossed the boundary lone
33
-: . ..-. ___ .. L..._. . . . . . . . . .
MIL-HDBK-781
mu,: be Iabelcd s,nce the ,lumber could not be read from the oral, nate After a reject occurs and correcl, ve
acl, on is approvee, the true plot should be returned 10 the boundary Itne. Conttnue the true P(OI IV realtime, .md sequentially number the subsequent failures ai shown on failure 16 of FIGuRE 36
4.8.4 Additional ali-eauiprnent production reliabilltv acceDlance Ieslplans, A unique all-eau, pmenl
test plan can be developed from any PRS.Tplan. On any given program the all-equipment test selectedshould be based on the accual sequential test plan used during the qualification phase. If ● sequential testwas not used during qualification, the procuring activity can select the most suitable plan. FIGuRES 37
through 44 provide all-equipment test plans which correspond to the PRST ptam given in 4.6 (lest Plans I-Dt’ I tects do not fo!!@w !he origin?! Wa!d formulaetb.r~g~h v! II-D). The a::epl and reject !jf?~. S! & $eo.,uer?.!a
(tee Reference 8). They ha.e bee. modified to account for the ●ffects on the test risks of truncation. Incomputing the all-equipment test plain, this modification was not made, therefore the accept and boundarylines of the all-equipment !est wil I not lineup with the accept and reject lines of the corresponding
$equential tect. The difference is in the distance bmwean the lines. It is felt the original Wald formulae (seeRefcf@itc6 8) which were computed withui c~r,sicfwir,g incncaticm, are mGrs?appropriate for irhe a!!-eqccipment plan~.
4.9 Reljabill!v estimate~from unit-level rewlts Astep-by.step wmmaryof theproceduce which can
huwdtocomtine te%tdata from fixed. duralionlests ora PRSTisprovided in4.9.land4.9.2. Thelechmque IS called the approximately optimum (AOJ method and is de$mbea in greater detail In References13, 14, and 15.
4.9.1 Calculation method. Thecalculalion procedure u%edinthe AOmethod isasspec#ftied4nathrough e.
a. Stepl. Verify method requirements Theconformance tolherequirement%of 1through5 should be.erified Anyviolatiomw illaffeci \heopl#mal#lyof the method.
1 Thepfocedute wa$deri.ed fersernes sub$yslem%; forpractocal purposes ilissuff, c,ent
that all subsystems are essent,al to ;ystem operation.2. Subsystems should eachexh#btt exponential failure dislrsbu1ions.
3. Subsystems should bestato%lically tindependent: that, s,thefailure of anyone subsystemwill not inducea Iailureof another wbsyslem. Inadditi on, lhere should benoappreciable fa!lurerate% due;G ir,:erftice$ (Flydrauli c:, cabllrng, !iziure;, a,-,d ;c fc,a,h).
4 Each 5ubsys1em mu5thave benlested separately unttfalleast one fatlure was
observed. Alltests must have been terminated at a failure. If Ihetesnw erelruncaleda fterag, vent line.
di5card allthe$uwival !imeafier thelaslfailure ofeach\ub$ystem Ifoneor morewb$ystems have nofailures, see 4.9,6.
5. Thettme loiailure ioreachsubsystem must be knownb. S1ep2. Initoal calculations. Calculate andverify thelotal number ofsubsystems tested. the
to!al number of failures of each subsystem, and the total time on test for ●ach subsystem.c. Step3: Parameter calculation. Calculate (m)and(v) u$inglhe following formulae:
u = + I(r, -1)/ Z~l+Z,jf,=,
34
MIL-HDBK-781
(.) afe as follows:
I
3 1 1 2 2 1.— +——— —9.919 15.966 + 26.897 + 26.511 + 62.439 + ~
= 0.3024 + 0.0625 + 0.0372 + 0.0754 + 0.0320 + 0.1008
= 0.6103
:- ,,.L, . ~ ,,. —l!/z:!+:z,; ;J
,=,
3 I I 2 2 1.—+98.387
—+—— ——255.872 723.449 + 702.833 + 3898.63 + 98.387
= 0.305 -r 0.0039 + 0.0014 + 0.0028 + 0.0005 + 0.0102
= 0.0493
Therefore:
m = 0.6103
u. 0.0493
At Ih#s Clmelt fsneces$ary Iodecideupon the level ofconf,dence(l - 0 ), Ie.el Ofsignifocance( O), w,th
whith ih~ iower bcwrml will be otiLaint. d:
AMu.me flrsl lhal a level of confidence of 7S pe,cem (lhal is. our estimated lower system rel,abil(ly bound)w!II !n fact be below the real $y,tem reliabil,ly value at least 75 percem of Ihe time given Ihe tolal Umes onIesl (ZJ) =) Snobla ined here, n. For this case, we look up lhe 751h percentile, n~, . a,, ,na slal, sl#Cal Iablefor the $lznd,irti~zeti fim,m~; ij#slr,&titwfi sad Gbcc,ifi:
’075= 0.6S
&swm, n5 thai the specif, ed mmsionlirne for thewhole system is & = 1000 hours (or t~ = 1.0), we calculatelhe AO rel, ab,l,ly bound as follows:
for n,, -~ = 0.68, that IS. a= 0.25 and Im = l. O(mis$iontime)
. UP[-1.O X 0.6t03(l -0.0493/9(0.6103)2+ 0.68~/310.6103JJ31
= exp[-O.6103 (1 – 0.0147 + 0.68 (0.2220)/ 1.8309 12]
= apI-o.6103 X 1.0678JI
. CTP i-u.743ul
= 0.-?76
MIL-fiDLIK-781
Another syslcm rel, abilily bound wh, ch will Le below the real ~yslem (el, abil, ty value only 50 pe,cent of theIimc can be @lcul ated as before, but now use, #n%lead, the 501h percentile In a standardized norm.il
distribution table. This value is. of course, zero This bound will be larger than the previous one vnce ,! WIIJ
bound the real system rellabtlily value a smaller percentage of the limes. It i$ obtaoned by repeaung theprocedure already described with the $ame parameler! (m) and (v), wnce it ii for Ihe same system. and the-me mission time (tm), since requirements for [ 8.) have not changed. and with the new percentile (n) :
for:
n ,,-=)-O. O, Lhafis, a -0.5. Im= 1.0
~,(~ ) = =P[ .-0.6103 (1 -0.0493 /9(0.6103fi + 0.0 -/3 (0.6103)131.
=crP[-. 0.61 O3(l - 0.0147 + 0)31
= up[-O.6103 X 0.985331
-apl-o.5ti38i
-0.558
4.9.3 The case of onlv one failure (n some wbwstem($) Considering the formulae for theparameters (m) and (v), we can easily conclude that for every subsystem (J) with only one observed fa,lure(that is, r)- 1 a O) the information pro.,ded by thi$ wbsys~?m 10 the rellabllily bound is zero (that ,s,
(~1- l)lZj = O). That w no matler what time a failure oLcu,scd ,n sub$ystem (I), the term {r] - IIIZ, vanishes anIhe equations for (m) and (v) and has no impact on the calculation of the AO rel, ab,lity bound (~s(t~)). Th, $
wa% particularly critical in the orlgtnal verwan of (m) and (.), (see Reference 13, Table 2. Formula 1), andcreated a need for the adaptive procedure Formula 1 refers to the special case where only one fanlure os
observed during lhe Iesttng of all subsystems mlegra!lng the syslem. The main problem w,th Formula 1 ,%that, when rl = 1 for 1 <j < n, the term:
~ (,, - l)/z: o
>(r, -1)/z2=iJ
whicl) is indeterminate (that IS, when each subsystem has experienced only one failure). W#lh the generalversion for (m) and (w) proposed tn References 14 and 15 and sugge%ted ,n those references as the most
appropriate Ont, thi$ Siluat, on does not ari$e, In fact. if r, = 1, 1 <j <n, lhen m = Z, and v = Z%~,e still wellde f,ned. We can appreciate also Ihe tmponance of renam, ng the subsystem with me smalle~l total ttme onlest among all wbsys! ems under cm-mderalion. as Z,, For this spec,al case, take the $ame numer,cal examplepresented in 4.9.2 and modified a%follows:
Subwstem 1 Subsystem 2 Sub5vslem 3
t, = 0.619 11 = 1.146 1, = 2.6897
11 = 0.7 12 = 1.6S
1~ = 0.9
[4 = 1.1
z, = 9.919 ZI = 15.996 Z, = 26.897
n, = 10 n2 = ]0 n~ = 10
r1=4 f>=2 r~=l
38
MIL-HDBK-781
where
~: = observed number of fa,lures for subsystem J
21 = total ume on test for subsystem I
Z(I) = least total time on test among k
k = total number of subsystems
Define the required confidence, (1 - a]. for the bound and the mission lime (tm) to which the bound will
apply.
d. Step 4: AO calculation. Calculate the AO $@tem reliability bound using the followingformula:
( “t,.e,fi ‘~’((m) . ap -Ire, xm l_A+—
9m2 3m )1
tm .
m,v =
(1-a] =Repeat d (step 4) for a$ many d, fferem confidence Ievel$ a$ are required, using the same (m, .) Th, s
compulaldon IS readily performed by Ihe FORTRAN program I)slting in 4.9.8. In this way sensitivity analyse$may be performed
e SIep 5: Calculale failure rate bound. An upper bound for the total system failure rale,may be found d,rectly from the AO reliability bound.
AO system reliability bound
mission time
parameters calculated in c (Step 3)
( 1- 0 )th per’emile point from the standardized normal distribuuon
required confidence
F,r$l. the system failure rate is e~limated by:
b b
0, =
8, =
MTBF =
-s ~,= i- e,-],=1 ,.1
syslem failure rate estimate
jth sub$ystem failure rate estimate
jth wbsfitern MTBF ●stimate ( = 1/ @j)
mean-time. between-failures
and where the ( ~,) may be computed from:
O,=r, !ZJ
Then, the upper bound on this failure rate is given by:
= -ln!lf II 11/1$., .,m
35
MIL-HDBK-7B1
where,
4.9.2
~, = IJPPe: bound on the \ystem failuce rate
In = natural logarithm function
Numerical emamoles. Numerical edamples have bden developed to illustrate the appl, cauon of
the AO acmroach and the ver, f,calaon of the model reauiremenls A comolete development from the data,—.collection %d reduction pha$e to the c?lculalion of lhe de$iwd AO bound will be presented
Assume that the system cannot be tested as a whole becauae of costs. Therefore, it$ n components o,integrated subsystems (for ●xample, S) will ba te$ted separately.
Assume that the conditions of the symem (cost. tize, and $o forth) limit t=ting to a reduced number (forexample, 10) of each subsystem (that is, nj = 10, 1 Sj s 5). Al$o, assume that these unit$ will be constantlymonitored and Ihat the failure times of each failed unit will be recorded accurately.
&sume that the sysIem as a whole has been designed 10 attain a spectif,ed upper test MTBF,( @o), of t 000hours and that all the times-lo. fa,lure of Ihe Item will be convened into units of this upper test MTBF byd,viding the life of all failed items by (go) Thi$ i$ a convenience, not a reqwrement. for the correctimplementation of thts methodology
Assume that for the example system we have actually observed the failure times (t,). ezp,essed <n un!t% of
( 80) listed in TABLE 18 For example. for Subsystem 1 there were (n, ] = 10unitssimultaneou$ly out on testand the f,rsl four failures occurred, respecl,.ely, atstand?mzed tfme~(t,)of 0.619.0.7, 09, and 1.1 (for , = 1,2, 3. 4) inuniu of( 8.) (Ihal ,s. at 619, 700,900, and 1100aclual Itfe hours) The lesl for Subsystem, 1 wa!
stopped at the time of the fourth faflure, 1100 actual life hour$, and the total lime on test for $.ubiy stem 1 ,jrecorded a%:
2,= ~f, +(lo_ 4),4
,=!
. 0.619. 0.7 + 0.9 +1,1 + (6x1.1)
. 9.919tn un!t~of [ f?o)
The total Iimeso” Ie$t (Z}), for subsystems, = 2.3, 4, and 5, were calculated inthe% ame manner and
Iabulated in TABLE !8.
Subsystem 1 yielded the smalle~t total I#me on lest. In general, at thiislage. an inspection should be madeand the sub$y stem w,th the $mallest total ome on lest (regardle$5 of total number of units, on test or Ia,led)
should be recorded and renamed as $.ubsy stem 1. Hence. it~ total time on lest WIII now become (Z(l)) Th, sstep is crucial 5ince the ordering of the smallest total time on test a$ anylhing other than (ZI!J) will changethe value of the lower bound An example of an error of this type is provided in 4.9.S. Om.e data collec~scmand reduct, on M performed, the ACI procedure can be used to obtain a lower bound, for [he rel,abii,ly of the
entire system. In order to calculate Ihe AO system reliability bound, u$e:
/{[1 ).ap( *fiJl
.In, xm 1–~+-> m
9m2
F#rsl calculale the parameters (m) anti (.) For the data appearing lnTABLE 18, lhe calcu!at, ons for (m) ana
36
MIL-HDBK-781
The syslem IS now composed only of $ub}ywems 1, 2 and 3. with lhe same number of failures and failure
tome% for Subsystems 1 and 2 as before. However, Subsystem 3 now ha$ only one failure at the truncauontime, 2.6897, tn un, ts of ( @o) (Ihal !$. ihe lesl was slopped at the llme Of the first failure).
Calculation of (m) and (v) are:
(4–1)+ (2-1) (1-l) 1—— .
“G 15.996 + 26.897 + 9.919
=0.3024+0.0625+0.0+0.1008
=0.4657
u= ~ (r,-l)/Z~+Zlj~,=!
(4–1) (2-I) (1–l) 1—— .
= % + 255.872 + 723.449 + 98.387
=0.0305 +0.0039 +0.0102
=0.0446
With the$e values of (m) and (v) we can calculate a SOpercent AO lower system reliability bound for the
%pecifwd mission time C?.= 1000 hours [tm = 1.0 in unic$ of @o). Thus:
(
%..,fi ‘~,(fm)= up “,-1 Xm l-&+—
9m2 .3m )1for tm= 1.0 andn, i-e, .o, lhafi$#n. o.5
R (f )=Upi -0.4657(1 -0.0446/8(0 .465712 +0.0)’1-.”,
=exPIO.46S7(l -0.022 .S)3J
-apt -0.4657x0.977231
=apl-o.4345]
=0.6476
Ta calculate the lower confidence bound for a level of significance of 7S percent. aPPly the procedure used
10 calculate a SO percent lower system reliability bound That is. for the 7Slh percentile,
n{, -a I = no,75 = 0.68. We have:
for tm, = l.Oand n:,. = = 0.68, that IS. a = 0.25
39
MIL-HDBK-781
.-.e,pl-O.46!\7{l ..0.0228 +0.)436/1.3971)3]
=crP1-O.4657 x 1.06003)
=cqd –0.5861:1
40.5562
4.9.4 An ●stimator of the failure rate UPDer bound. Oflen. reliability engineem wein:ewstedin the
estimated $ysfem failure rale ($) as well as in the ewimated reliability (R,(t~)] of the system, given a mi>}iontime (A).
Assuming that d!, the conditions are met and following the notation of Reference 13:
n
0,=:$,=5 [1-’-),=1 )=:
where,
$, = ]thtub~y~~emfailurerate
@i = jlhwbsystem MTBF
AI here fore, .m esumator ( @$) of the upper bound for the total $ysiem failure rate ( ~~ will be.
4, –bdit,lfm)l/fm
where (R,it~)) ',[he AOes!imator of the$ystem reliabili tylower bound calculated !n4.9.1and 4.92: (tm) islhespecif, edtitlission timeand (ln)osthe natural logarithm. This(~%] failure rate upper bound lssublecttothe same constraints used in obtaining (R,(tm)), that is, mme level of confidence, dependence on \ame totallime% ontesl(Zo). an~allother constra, nt$d8scussed. hanilluslration ofthtsprocedure, assume we want toobtain an estimable of the upper bound of system failure rate ( ~,) for the two examples developed ,C.4.9.1and 492. Examples area! specifledinaandb:
a. Forlhecalculation method, whe,ethe letielof con fidence was7Spercen:.
$’= _ln+ .0.74296 failures perlOOOhn. rs
tsa75 percent upper confidence bound fortotal sfitemfail urerafe (that, s,lhisbound will be larger thanthe actual system failure rate at Iea\t 75 percent of the time).
b. Forlhesecond example. where ihelevcl ofconfidence wa\50~rcent, we have:
$,. .[” = .0.58375 faifumper 1000 hours
that is. the actual system failure rate ( ~,) will be enceeded by the above estimate ( ~,) al least SOpercen: of
the ttme.
4,9.5 Denarlures from AOmethod requirements Cauuons regarding lheuseofthe AO
method ologyandwggest, ons fordeal, ngw, thdev!a t,onsfr omthereq uirement$ area$prov, ded #na
through f:
40
MIL-HDBK-781
I
I
a. Theexponenttal! !yo{lhe stattst, caldj%tribut$on otthettmes-!o-f ailureandlheindependence of Ihewbsyslem$%hould be carefully checked 8othreq ubrements represent ,dealconditiom
However, lheycan bejusti f,edbnprac! ice. Forexample, lheexponenloal distribution requirement can be
justified byus,ng burn. tnandquallty control procedures forthe%ubsystem "scritlcal components Thesubsystem’s independence requirement can rejustified by the technical knowledge that actual subsysteminterfaces negi, giblyaffecl reliability. When either oflhe\e twocOndilion! isgravely suspecl, thepre$ent
AO procedure should nol be apphed. If ii is absolutely necessary KOu\e the present AO procedure, thenextreme caution if required and Ihe results $hould be interpreted with great care.
b. This caution relates tothelerminaliO ntime$Ofthe different ~ub~Y~temte$1~. Aflle$tsshould be failure truncated, lhatis, terminated attheoccurrence ofafailure [Type llcensoring). Mix:uresofTypes land llcenwring $chemes arenotrecommendad. lf, inagiven ~ub$y$tem le%thel esllruncallOntime
is other lhan a failure time, it is recommended that the last failure time before truncation be taken as theactual truncation time (5ee 4.9.1)
c. Theordering of thedata i$veryimpotianl forthecOrrect ~pplicalion of the AO procedure.Thesub$y\tem withthe least total tfmeontesl mu$talways rerecorded aiSub!ystem I,andits tota! timeontest, (Z(, )), included, nthelas: lermsof thecalculaliOn Of(m)and (v)parame1ers Aneaample of theconsequences fornoncompl, ancewi!h this requirement ispresented on TA9LES 19and20 Observe howlherewlts vary conwoerably due 10 (Z(I)) nol be, ng the lea~l 10tal time On le~l am0n9 the sub~yslem$.
d. The AOa?proach requires theob5ervat@on ofalleast one failure bneach$ub%ystem Thtst%averyslr!cl requirement andamust forlhecorrecl application ofthis AOprwedure. When deai, ng withh!gh-co%t, ultrarellable systems, the nece$sary lime to obtain a failure in some of the component subsystemsmay be too long Al$o, lhenumber ofitems onteslfor ag,ven%ub$ystem toobta, nah!ghprobabi l,tyof
gett#ng afailure be forelruncat,on timemaybetoosmall. Inpraclice, forsome pan,cular subsystem. leslingmay have 10 be germinated before obferving the first failure, but an engineering assessment is still reqwred.
e Under the real life constraints of d, the use of an adaptive procedure WIII be requtred inorder toprovide agrossapproxtmat, on forlhesyslem reliability bound A5wmethal af#rsl failure hasoccurred at the t,me of lest truncation (for the subsystem wilhout any prior observed Ia,lu red and calculatelhelowPr AOsyslem reliabil#ly bound. This will provide agrosslower bound forthe AOsystem reliability
bound. Careshould betaken nollouse lhisprocedure where lhetolal limeonles: forthesubsys!em !%lhesmallest (that is, 2(,1).
f. G,venthe formu;ae for(m) and(v), inthecase ofonereal orimaginary failure #nany Jthsubsystem, then r)- 1 = Oand (r,- 1)/2, = O. There fore, theinformalion conlribut ion of lhossubW$lem10the reliability bound ,$ nul!. de%% II is Ihe one with the smallest total lime on tesl.
4.9.6 Noobmrvedfattures Anexample of theadaptive procedure fordealing wi1h1hecase0fn0obser.ed la,lures fol%Ome subsystem #sprovnded below (see Reference 13). Aswmema: iorlheseconosubsystem, Ihe test was lermnnated before the I,rst failure occurred, that is:
Z, = 17.607 22= 20.045 23.33.644 Z4= 51.495
n,=2 nl=l n3=2 n4=3
2s= 82.214
n~=3
Exac1(90percent con fidence) bound = 0.726. AObound = 0.735 (a190percent con fidence level)
Assume that for Subsystem 2, the tesl was truncated before the first failure had occurred and the
corresponding lolallime ontes:!or Subsystem 2allhelruncat80n timewa%Z2 . 19.5
A$.umethal one failure hadoccurred alth#slruncal#on 1ime Thegross lower bound tsobta8neda$A0bound = 0.719 (a190percen1 con fddence level)
41
MIL-HDBK-781
4.97 rvDe I censor, nq ‘ocmwder ,! w}! wuncated. ]t ott,?, lhana Id,:ure l,me, a,wme !ha: :11;
Sub>yslem 3 lest was lruncated some tame .+!ler Ihef, fst fatlure but before the secood fa,lure. as aep, cled IVFIGLJRE 45. Had we wa, ted to observe Ihesecond Iailwe. the value$ obla, nec! according 10 Reference 13
would be
Z, = 14.61 z~ = 35.971 Z> = 62,542
n,=2 n~=Z n,=3
Exacf (90 percen!) bound = 0.731, AO bound = 0.738 (at 90 percent confidence level)
If we assume that the truncation time wa! (T”), the valuea obtained up to the first failure (that is, neglecong
test time from the first failure UP 10 lime (T”)) wOufd ~:
ZI = 14.61 z~ = 3s.971 Zj = 30.0
n,=2 n1=2 n3=l
The result is AO bound = 0.781 (al 90 percent confidence level)
An alternative adaptive procedure Ii to afwme that time (T”) i$ the lime of the second (la\t) observedfailure. This i$ not recommended because of the conditions specified in a through c:
a There are existing failures in the Ie$l other than at (1. )
b. Stnce the second following failure time will never be known. we maybe ,ntroduc, ngunnecessary b!as in the analy$i\ by as$uming (T”) IO be a failure l.lme
c. Stali$ucal properue$ of the bound are unnecessarily IOSI when Iruncauon M taken al anyother !imelhan al a failure
4.9.8 Computer program A comptiler program was wrbtten 10 #mplemenl the AO methodologyFORTRAN listings are Included #n FIGuRES 152 through 1S4. The program is se! f-contatned and may be
adapled for any computer with a FORTRAN compiler. The use of the program requ, res the data spectf,ed inathroughc:
a lnpuls:
k = number of subsystems
z, = total lime on lest for the subsyslem with least Iolal lime on le\l
n,(j) = number of failure~ of the $ame (previous) subsystem
28 = 2 s i s k total time on test for ith system
Wi$l = total number 01 failures for ith tymem
b = mmsion time desired In the reliability bound
P= percentile of the confidence level desired in the reliability bound
b OutPUIS:
M 1 = parameler~
VI = parameter$
42
-.. , -- . .. . ------ . . . . . . .. . - .---..--, ------ ._ .._- .-. . . . . . . .
MIL.HDBK-781
V42 = parameters
V2 = parameter
M3 = parameters
V3 = parameters
c. Reliability boundi: Of the$e rewlls, only the recommended values M2, V2, and thecorresponding bound are presently printed. The other rewlt$ are in fened as comments in the program. Theu$er may activate them easily by removing the commem command, An example run for the data provided inTABLE 21 is given in TABLE 22,
I
I
43
—. ,.. . .,, ,-
MIL-HDBK-7B1
5 COMBINE DE NVIRONMEt* rAL TEST CONDITIONS
5.1 - 5ect#on 5prov1des guidarlce loindivlduali responsible forestabl#shing tllecomb, nedenvironmental tesicond !t, o,lsused inrelia b,lnlyte%ls conduCled in accordance wllh MI L-STD.781 Tne data
i$pre$ented inamanner wt,lche ncourages laifort ngtospeci ficsystems, platforms, andoperat, o”alenvironment
5.1.1 ~. 5ection 5di$cusses thecom&nd environmenml teslcondal,ons lobeappl,ed dur(ng thereliaMl ltyte$t pr~rams specified tnTask$ 2OO.3OOand4OOof MIL-STD-781. Theanaly$esneededmestablish the appropriate test conditions are provided also.
5.2 Mission andlile-cvcle environmental orofile$ and1e$tconditions. Mission andlife.cycleenvironmental profiles and lest conditions are as provided in 5.2.1 and 5.2.2.
5.2.1 Msssion andlife-cvcle environmental DrOfileS Themission pro files should beused todeterminethe environmental $pecificauons and should be derived from the operational life profile de f!ned by the
equipment orsystem operatmnal requ, rement$ Ifth,$inlormation isnotpro.,ded inlheongtnalcontractual documentahon, prow%$on should be made for the procuring acliuity and the contractor IOcoopera tivelyd erivelhe miss#on pro f,le$and lheequl pmenlenvt ronmental specifocalaons Thlsder,. al, on
should make use of historical data on wm,lar equipmenl applications and mounting platform$ and ihe effectof equipmenllocation intheplatform should be accounted for. Each signif, canllife-cycle event must beconsidered, inciuO, ngtransponalton. handl, ng, ,nstallal#on andcheckoul. and1ac1lcal mtwon%,ncludhngplatform cfitegory and operauonal situal, on
5.2.2 Envuronmerltal le%lcond,ltons Thereltab!Ii tygrov+th. qualification, andaccep\ancetes!\ihouldbe performed under lhecomb, ned ,nfluenceof ●lectr ical ,wwer Input, Iemperal ure, vhbrat, on.hum,djty andolher appropriate lest cond,l, om Thelesl le.e!afor these lest cond, t&ons$hould beder,.ed
from theeq"ipment's miss&onanaen., ronmentalprof, fe$ When lheequipmenl, sdesigned for one
aPPfiCatiOn, with a single mission, or one type of repetitive mhssion. there is a one.: o.one relatlomh!~between thetest pro file andmisslon andl, fe-cycle environmental pro fife. Thelesl condil, onsshould$imulate lheactua !stresslevel sdur,nglhem, won Iftheeiau, pmenlis designed forseveral m,wonsandenwronmenta! cond,l, ens, \he lest prol,le should rep fesenl a composite of those missions, w,th the tesl
levels and durauom being prora~ed accord~ng 10 the percentage of each m85sion type expected dur~ng Ihe
equipment’% liie cycle fnorder toaer, uereal, %loctest condtt#ons andlevels. the actual environments
(especially temperature andvibrailon) should remeasured althelocat!on where theequtpmen:lstobemounted dunngana ctualmiwonoperauon Whelesuch data arenolavailabIe, Ihecond# ttons and levelspresented ,n S.3 lhrough 5.1 O.I.4 may be used asgu,deltnes
5.3 Combined env, ronments fo, f,xed.o~ound equipment. Equipments dewgned forl, xed.grounainstallation, are generally located bn a conuolleci enwronmem wi~hin a building and, therefore. do not
require cyclic env&ronmenlal test! ng [see Reference 16). However, $ince Ih8sequtpment mus1be1ransponeG10 the final installation si!e, a nom, nal .ibrauon tesl ;hould be applied, wllh power OFF, before eachreliability test. Contractual lyspeci f!coperal!ng crlter!a based ontheguidel, nesin5.3.l through 5.3.4 maybe
used inthetest olanandprocedure$ Atyp, calcomblned environmental teslproflle for fixed -gro"nd
●quipment isshownrn FlGURE46 Theduratlon of theprofile isnormally 24hours oranevenly divisiblefraclion thereof,
5.3.1 Electronic sIres!anddut~c~cle Theequipment should beoperated atnominal design inpulvollaae f0r50Dercen10f the time and 250ercentof thetime each atmunimum andmaximuminwtvolta~e$. The;nput vollagerange. if notipeci f,ed, should be 27percent of thenominal lnputv01tage The
duration of Ihe operating cycle should depend on the operational use of the equipment; typically. four
hours, eighlhours. or 16hours perday. oraround. the-cloc hcont8nuous operation with period#cshu! aowns
forrouune maintenance should becorwdered Theequipmenl dutYc Yclesl]ould be Of:aboul 9Opercen1ol
Ihe testcycle The OF Fper!ods should be randomly selected
44
MIL-HDBK-781
5.3.2 V, brat ion $tres$ Normally, vib:ation 51re%%teWn9 i} nOl required during the OPeral,Onal phaseof the enwronmenml moflle. I( the e.auiumenl il not packaged $peciflcallv for transponat!on to theInstallation stte, a nommal .ibrahon $Ire$i consisting of a single-frequency sine-wave vi bralion a!
2.2 gravitational acceleration unm peak (g’s pk) aI a nonre~onan! frequency between 20 hertz (Hz) and60 Hz, should be appl,ed for 20 minute$ before $tarting the reliability test. If the equ!pment has L specified!htpping configuration. it should be qualified for adequate $htpping protection by packtng it in that
configuration and testing it prior 10 the reliability te~l in accordance with the shipping vibration and $hochexpected. Establiih the vibration test requirements for ●quipment transposed as cargo in accordance withthe maximum values of MIL-STD-810, Method 514.3, as !pecified in a through c:
a. Basic tran$pofl; Test Procedure 1,Test Condition 1.3.2.1b. Lar9e a$sembly traniport: Ten Procedure Ill, Test Condition 1-3.2.2c. Loose cargo Iran$pon: Test Procedure 11,Te$t Condition I-3.2.3
5.3.3 Thermal stres%. The equipment should be operated at itf specified ambient temperature. If notspecified. use these thermal conditions provided in a through e:
a. Cold soak temperature: -5a”c
b Hot soak temperature: + 85°Cc. I{ the equ, pmenl is installed in an occupied building with automatically convol led atc -
conditioning and heating, use 25°C as the operating ambient temperature. Computer ecwpmenl should becontrolled at 20”C
d. If the equipment i$ installed in a nonair-conditioned building where summer heal may
reach a high lemperalure, use 40”C as the operating amb, em temperature.e. If the equ, pmenl IS ,n an unoccupied, nonair.conditioned enclosure and in semitropical or
trop,cal Iocat, ens. perform one-half of the lesttng al 60”C, one-quaner at 4LTC. and one-quaner al 20’C.
5.36 Humtdtlk. Humld,ly test,ng IS not required unless specifted in the conlracl. See AR70-38 foradditional guidance Ior humtdity lesung
5 a Comb,ne’S env, ronmen:s for mobile around eauipmenl. This calegory of equipmenl includes
wheeled veh, cles, Iraci. ed vehscl es. $heller con ftguratmn%, and manpacks ($ee Relerence 16) The specllnc
equipment application should be considered when specifying the comb, ned enwronmenrs for rellab,l, tytewng MIL. STD.210 and AR70.38 should be used 10 define the climalic extremes for the geographical area,n wh, ch the equipment and vehicle will be used. and MI L-STD.810 can provide guidance for the .ibrauonrequ, remem% Equipment operaung on moving platforms, includ!ng wheeled and tracked vehicles, andwh,le !tauo nary, should be considered In developing a cyclic test sim!lar to Ihe !est shown m FIGURE 4?. TheIe\! ptol,le durauon $hou!d be 24 hours or an evenly d,wsible fraction Ihefeof The chmauc ealreme andMI L.5TO.81O ., brat, on data should be considered 10 represenl max#mum Condll$on$ The aC1ual lesl
environmenlaj condn lions should onclude a distribution of values which reflect% e,pec ted Cond,ltons Only asmall fractmn of lest levels should reach the maximum condltion$.
5.4.1 Electrical stress and dutv cycle. The equipmenl should be operated al nominal ales, gn onpdtvollage for SO percent of the ON t,me. at minimum voltage for 25 percent of the ON time, and at max, mumvoltage for 25 percent of the ON ume. The input voltage range, if not specifoed el$ewhere, should be as
specifted an a through d:
a.
activity
b.acflviIy
c.acttw:y
d
Wheeled vehicle equipment: 210 percent of nominal or as specified by the Procuring
Tricked vehicle equipment: ? 10 percenl of nomtnal or a%$pecif,ed by the procuring
Sheller Conisguration equipment: z 10 percenl of nomtnal CMas spec,f,ed b] tne pro;ur, ng
ManDach eau, pment: For2A vol!$d, rect current (VDC). volt% (V) maa, mum = 32 v.m,n, mum = 20V
45
.
MIL-HDBK-781
1.
5.5.1 .1,1 Electrical stress and dutv cvcle. During the operating cycle, input voltage should be variedbetween several levels as shown in FIGURES 48 and 49. Unless other.vise spacified by the procuring activity,the input voltage range should be 27 percent of nominal dtign voltage. After reference rneaWremWM5
are taken at nominal voltage and room temperature. minimum and mazimum voltage should be appliedduring the operating cycle as $hown in FIGURES 46and 49. The duty cycle is given also in FIGuRES 47 and 48.The ●quipment should be OFF about IO percent of the time. F’owar should be ON during the cold and hot
$oak periods.
5.5.1.1.2 Vibration $trecs. The vibration stretc should be applied .?ccording to the schedule inFIGURES 48 and 49 on a 25 percent randomly aalacted duty cycle. The vibration apactra should have the
shape definad in FIGuRE 54. The teat should be run ona single ●xis Cpecified by the procuring activity.
5.5.1 .1.3 Temoeralure and humidity stre$$. The suggested temperature and humidity profile for●eternally mounted equipment i$ provided in a Vwcwgh o bale.w. Ail relative humiathy (RH) values are
t 5 percent (RH):
a. Starting from 22*C and 25 percent to 75 percent RH. lower the temperature to -50”C asrapidly as poa$ible, hold at -5fYc (cold wak) for 1.75 houra (ON). Raiae the temperature to -3~C. Apply thecold soak only during the first three cycle%
b. Slowly lower the temperature to -34.5°C over a period of 3.5 hours.
c. Slowly raise the temperature to -2&C o.er a period of 13 hours.d. Rai$e the temperature to 22’C over a period of 5 hour$.
e. Hold the temperature at 27C, but bring the RH to 25 Wrcem to 75 percent over aperiod of 1 hour.
f. Raise the temperature to 25*C and the RH to 95 percent over a period of 2 hours.
g. Over the next 10 hour% slowly raise the temperature to 29°C with the RF! keptcontinuously at 95 percent and hold for 5 hours.
h. Slowly lower the temperature to 25*C over a period of the nefi 5 hours with the RHkept continuoudy at 9S percent,
i. After 2 hours, lower the temperature to 2~C ●nd the RH from 2S percent to75 percent.
j. After 2 hours, raise the temperature to 2YC with an RH of 6S percent.k. Over the next 12 hours, raise the temperature dowl y to 4WC with an Rli of 25 percent
and hold for 2 hours.1. Raiw the temperature to 65-C (ON) and raise the RH to 95 percent and hold for
2 hours. Drop the temperature to 48”C. Apply the hot coak only during the f!rst three cyclesm. Over the next 9 hours, slowly lower the temperature to 22°C and bring the RH to
25 percent to 7S percent.n. Repeat steps f through I six times.
o. Return to step a and repeat the cycle until the desired test duration i5 obtained.
Hot and cold soaks are added to cover wor~case storage and tran$f%mation ●nvironments.
S.5.1.2 Internally mounted eauipment. Tha full profile for internally MOWW?CI equipment is asshown on FIGURES 50 and S1.
5.5.1.2.1 Electrical str~$ and dutv cycle, Tha electrical stress and duty cycle 5hall conform toS.s. }.t.l.
5.5.1.2.2 Vibra!ion stress. The vibration stress should conform to 5.5.1.1.2.
5.5.1 .2.3 Temperature and humidity stress. The temperature and humidity stress profile forinfernally mounted equipment is as %pecif, ed in a through m:
47
MIL-HDBK-781
a Starting from z2°C and 25 percent1075 percem RH, lower the temperature to -50°C airapidly M powble and hold at-50”C ((old soak) for 1.75 hours (OFF). Raise (he temperature to O-C a! rapidly
a%oowib le. ADDIV the cold soak onlv for f!rsl three cvcles
for 5 hours.
for 6 hours
b.
c.d.●.
f.
9.h.i.
1.
Hold O-C (OI 195 hours, then raise the temperature m 19-C over a period O( 2 hours
Over a period of 1 hour, establish conditions of 2PC and 25 percent to 75 percent RHOver a period of 2 hours, establish conditions of 37°C and SO parcem RH.
Slowly during !he next 10 hours. emabli$h conditions of 41-C and 48 percent RH; hold
Slowly during a period of 5 hours, ●stabli$h conditions of 37°C and 50 percent RH.Hold 3TC for the-next 1 hours, but lower the FtH to43 percent.
After 2 hourt ●stablish conditionsof41 ●C ●nd 33 percent RH.Slowly during the next 9 hours. e$tablish condifion$ of 50”C and 21 percent RH; hold
Repidly rai$e the temperature to 65°C and the RH to 95 percent; hold for 2 hours (OFF).Lower temperature as rapidly as pos$ible to SO-C. Apply the hot -k only during the Iimt three cycles.
k. Over the next 5 hour%, dowly establish conditions of 22-C and 25 percent to
75 percent Rt+1. Repeal ftepf d through j six bmesm. Relurn to step a and repeal cycle unul the desired test duration is obtained.
5.5.1.3 Inlernallv mounted eauiDmenl. tern oerature controlled $Dace. 5ee FIGURES 52 and 53 for
the full profile of the Internally mounted ●quipment for temperature controlled $pace.
5,5.1.3.1 Electrical stress and dulv cvcle The electrical stress and duly cycle for internally mountedequipment In a temperature controlled space should conform to 5.5 1 1 1.
5.5.1 .3.2 Vibration stress The wbrahon stress should conform to 5.5.1.1.2.
5.5.1 .3.3 Temoeralure and humid,lv stress oroflle The temperature and humidity stress profile for
tntt, rnally mounted equipment in temperature controlled $paces is provided in a through i;
a Staning from 22’C and 25 percent to 75 percent RH. lower the temperature as rap,dly& pos$ible to -5WC (cold $oak) and 25 perceni RH; hold for 1.75 hours (OFF). Raise the temperature to 22°Cas rapidly as possible Return the RH to 75 percent Apply the cold soak only during the fnrst three cycles.
b. Slowly over a period of 1S hours, establl$h condition$ of 2YC and 30 percent RF!.
c. 510wly over a period of 7 hours. e$labliih conditions of 2YC and 30 percenl RHd. Repeat stegs a through c sir times
e. Lower the temperature to O“C in 1 hour; hold for 5 hour%.f. Afler 2 houm, e$labltih cond, tiom of 20-C a“d e6 percem RH: hold for 6 hours
g. After 2 hours, establmh condiuom of 5WC and 21 percent RH: hold for 4 hours Raise
the temperature as rapidly as po!sible to 65-C; hold for 2 hours [OFF). Decrease the temperature rap!dly to5~C. Apply the hot soak on only the fir$l three cycles
h. Afler 2 hours. ●stabl, sh condniom of 22-C and 25 percent1075 percent RH.i. Return to slepa and repeal the cycle until lhe desired test duration if obtained.
5.5.2 Naval submarine. The submarine profiles should be based on a 24-hour test cycle which shouldbe repeated for the duratron o! the test (See Reference 18).
5.5.2.1 Electrical and dutv cvcle !Ires$ During the operating cycle, the input vollage $hould bevaried between several levels as shown ,n FIGURE 55 Unless otherwi$e specified, the input voltage range
should be 27 percent of nominal Reference measurements should be made at nominal voltage and roomtemperature. Mtn!mum vollage should be appl)ed for the initial period of the operating cycle and maximum
voltage should be applied dur, ng the pertod of highest ambient temperature Nomjnal voltage should be
applled for the balance Of the cycle and the du!ycycle ihould be as shown in FIGURE 55,
48
I
MIL-HDBK-781
5.5.2.2 Vibralion sirm$ Submarine vibralion $tres Ievel$ are normally extremely low. However,since vibration Ievel$ after battle damage and during transportanon may be considerably higher, thevibration stress of FIGuRE S4 should be wed with the profile shown in FIGuRE 5S. The actual vi brauon time
should be 3 hours in a 24-hour test cycle. Thi! test should be run on a single asisselected by the procur, ngact! vily. The battle damage spectrum $hou!d be applied for 10 minutes during each 2d.hour test cycle al thestan of the vibration cycling. The Iran$portation spectrum thould be applied for the rema, ncler of Ihe3 hours, in 20-minufe interval$, with 10-minute breaks.
5.5.2.3 Temiwrature and humiditv$trei! Drofile. The temperature and humidity Krm$ profile forNaval siibrrlarine equipment; i; prcY&?ed in a :h:euQh k:
a. Starting from 22°C and 25 percent to 75 percent RH, lower the temperature a~ rapidly aspossible to -SO-C and hold for t.75 hourf (OFF). Apply the cufd $oak only on the fm~t three cycles
b. Raise the temperature to -35’C; hold for 2 hour\.c. Kaiw the temperature to IYC: hofd {or 2 hoursd. Raiae the temperature to 2rC; hold for 6 hours.e. Rai$e the temperature to 5WC and the RU 1095 percent; hold for 1 hour.f. Raise the temperature to 65’c; hold for 2 hours (OFF). Hold the RH at 95 percent Apply
the hot soak only during the firsl three cyde$.
9. Lower the temperature to 50”C and the Rti to 65 percent; hold for 2 hours.h. Lower the temperature 1022.C and raise the RH to 95 percent; hold for 4 hours.i. Lower the temperature to O.C and lower the RH to the 25 percent to 75 percent range.
1. Lower the temperature to -35°C over a period of 2 hours; hold the RH in the 25 percentto 75 percent range for I hour.
k. Repeat the tesf p,of,le as direclti by the Program Manager.
5.5.2.4 ~. Mo, slure levels are not a significant $tres! factor for equipment installed Inprotected areas on wbmar, nes For equipmenl which may not be properly protected during Iransponationand storage, constilt MI L-STO.21O s.nd .4 R?0-3B for da!? en envi?onme fital e~tremes.
5.5.3 Marine crab (Armk) Mar;ne craft includes a variety of smaller craft wch as Iandlng crati and\maller vessels used on interior waterways, The environmental slrus cycle for marine wah ISg,ven mFIGuRE 56 (see Reference 16) The te$! cycle duration should be 24 hews or an evenly divisible fraction
thweol. 7he erwircmmtertis fix ieiiii,Y $,t-oSiitmaii~~ uafi a.? @ven Ifi 5.5.3.1 ihlGugh 5 S 34
5.5.3.1 Thermal stre~! Unlew otherwise specified by the prwuring activity, the marine crafl thermalstress environment should be constructed from a combination of the environmenwm TABLE 23.
5.5.3.2 Vibration $tres!. Guidance for establishing vibration tem requtrement$ M provided inMIL. STD.8 10, Method 5.14.3. Test Procedwe 1,Test Condition I-3.2.1 1. If the vibrallon is unknown or not
specifted, the requirements provided in a through c should be used:
a. Amplitude, .020 inch (DA) t .004 inch (DA)
b. Frequency range: 4 Hz to 33 Hz to 4 Hzc. Sweep time: 10 minutes ? 2 m#nutes (up and down)
5.5.3.3 Electrical stress and dutv cvcle. A voltage variation of ? 10 percent ii normal for mar,ne craftP Iyp, cal profile would be: 25 percent of the time al nominal + 10 percent; 25 pefcenl of the time alnominal -10 percent; and 50 percent of the time at nominal. Unle$$ otherwise specified by the procurtngacliwly, the duty cycle of input power should be 10 pe,cent OFF and 90 percent ON, in a preselecle~irregular patter”,
49
MIL-HDBK-781
S.S. Q Underwater vehicles En.ironmenla! test data whicl~,% appropriate for the rel, ab,l, !y test, ng ofunderwater .eh,cle$ usDre5enled in Reference 19. Government program N4anagers and equipmentdevelopers are referred 10 Reference 19 lot appropriate test data It should be noted that the data an thisreport applies only to the MK.50 Iorpeao; other %y$tem%may require extrapolation of data.
5.6 Combined environments for iel aircrah eauigmenl. A combined+ nvironmenls test cycle shouldbe used whenever pos$ible for testing jet alrcrah equipment. During thi$cycle the thermal stress, vibration.humidity, and input voltage imposed on Ihe lest item should be varied simultaneously. The speciftc te$l
conditions will ba determined by the type of aircraft into which the equipment is to be instal lad, its Iocat, onwithin the aircraft, the aircraft mission profiles, the equipment class designation (in ●ccordance withM IL-E-5400), i ype of cooling f or the compartment in which the equipment i~ located (air-conditioned or ramair.cooled), and the type of equipment cooling (ambient or supplemental air) which i\ being used (see
Reference 20).
5.6. t M, fsion orofiles. Each aircraft type is de$igned Iooperate within a Jpacific flight ●nvelope and10 fly specific mission profiles. The environmental profiles used lot-t prototype and production aircrafishould be based on these flight envelopei and profile$. When de$lgn flight envelopes and flight m,$s, ocprofiles are not available, the generalized flight envelope~ in FIGuRES 57 through 62, and the tablesincorporated into those I,gures, \hould be used for developing mowon pro fnles (altnude and speed ve, w$
t,me) for spec, ftic aircrah types. From the~e m,ssion profiles, reasonable and practical environmental te$tprofiles may ba developed. The mission profiles are clastif!ed by $pecial aspects such a$ phaie alu:ude, pha~e
Mach number, phase duration. and lran$ition rates between steady-state conditmns. If mission proftleinformation is not available. the data in 5.6.2 through 5.6.2.8 should be used to establi~h the enwronmenlaltest condltiom
5.6.2 Environmental test orof,le$ The test profile should be developed from the aircraft miss, onprofile, The condtt!ons which must be deftned are temperature, vibrat!on, humidi!y, and inpul vollage
Each test cycle should consist of Iwo m,smons One mission should start in a cold environment and proceedto a hot environment; the second m,smon should start on a hot enwronment and return to a cold
environment. The mission profile should be analyzed to determine the ●nvironmental stress levels for each
of the mission Ilighl phase$ (Iakeoff, chmb, combat, landing, and so forth) as well as for ground cond, uomIn addition to the information derived from the m,won profile, the data specifoed in a through d should be
compiled.
a. Equipment clas$ (see MIL-E.5400)
b. Equipment Iocat!on within the aircraftc. Type of cool, ng for the compaflment in which the equipment is located (air-cond, tinned or
ram air-cooled)
d. Type of equipment cool, ng (ambient or supplemental air)
A table of environmental profile data should be prepared for the specific aircraft and equipment under
consideration. This tabulation $hould include the data specif ted in e through p:
● ✎
f.
9h.
i.
i.k.1.m
n
0
P.
Mission phajeDuratitm (mmutes)
Altitude (thou$ands of feel)Mach number
Companmem temperature (“C)Temperature rale of change ~C per minute)
Dynamic preswre q (pounds per $quare foot ( Ibs/ ftz))Power spectral density (P5D), WO(g2 /liz) = K(q)?, where q = dynamic P~e$wreP5D, W1(gZ/Hz) = WO-3 dBHumtdily
Equipment operauonInput voltage
50
—
I
MIL-HDBK-781
A typical environmental profile data set for ●quipment attached to structure adjacent to the externalsurface of a ,et. propelled Navy attack aircrati i$given in TABLE 24 Source$ from which environmental data
can be obtained and the methodology 10 be used in entering this data in the table areas provided in S.6.2. 1through 5.6.2.8. The methodology describes how each $tre$s level should be obiained and prewmm that nomea$ured data. either specific or for similar applications, i$available. (f meawred stress-ievel data ($peciftc or
$imilar) is available, it should be entered directly inlo TABLE 24. TABLE 2S should then be developed by
aPPlying the special vibration and !hermal wound rules as Provided in 5.6.2.1 through 5.6.5.5.
5.6.2.1 Mts$ion ohase (Iemoeralure mode). The specific mi$$ion phases should be der(ved from themi$\ion profile. The number, type, ●nd duration of the phase are functions of aircraft type. The ground
condition$ wed for all aircrafl and equipment typm should include a nonoperating pariod followed by aperiod of operation. Since the equipment often will beat ●ithar a low or a high temperature when in a non-
operating mode and turn-on will occur w~le it i$ still at that tkrmal condition, both hol and cold start>should be included in the teat profile.
5.6.2.2 Duration Theduration of each mission flight phase should be obtained from the m,ssionprofile. The test time for g,ound conditions should apply to all aircrah types and missions The test tdme fornonopera:lng and operat, ng Iemperawres it 30 minutes.
5.6.2.3 Altitude and Mach number. Altitude and Mach number should ba obtained from the missionprof!le analysis.
5.6.2.4 Commanmenl Iemoerawe The information specified in a through i should be obtainedpno? to eitabh$h, ng !he companmen! lemperalwe levels;
@&
a Ahtl”oe and Mach number
b. Equ, pment clas! in accordance
c
d
e
f.
9
h
w,th MI L-E-5400
Equtpmenf coobngmethod (amb!ent or
supplemental)
Companment coolingmethod (a!r-conditioned
or ram a,r-cooled)Power d,s,ipation
Equipment density incompanmem [crowded
or uncrowded)Aer flow into
companmencTemperature of
air flowlng intocompartment
i. Compartment
area exposed
~
Mandatory
Mandatory
Mandatory
Mandatory
De$irable
De$irabie
De$irable
Desirable
Obta, ned from
Mission profde analysi}
(see5 6 2.3)Equipment ales,gn
control spec,l, cation
Equipment designcontrol specification
Equioment designconfrol $peci I;cal,on
EquiDment dewgncontrol $pecif, cation
Aw-condit@nad
des!gnspeciftcation
Thermal design
specificationThermal design
specification
Aircrah design
spacif, cation
5.6.24. ! Ambient-cooled eauioment The data for amb,ent. cooled equapment are prowded in a
through b (3]:
51
.- .-., ... , ,_&., _A.-1..%. —_
MIL-HDF3K.781
a. !iol. daylemperatur ?: Using the allmde. Mach number, the MI L. E.5400 Class, a~dcompartment cocdtng ,nformatlon, enter TABLE 26.27. or 28 as appropriate m determ, ne hot-day
compartment temperatures for each of the miwon fltght phases For the gro,und conditions (nonoperattnqand operating), a temperature of + 55.C sl,ould be used for Cla\s I equipment and + 71-C for Clas! IIequipment
b. Cold-day temperawre: Cold-day companmenl lemperature$ for equipment an ramaw-cooled compartment! !hould be wlected from TABLE 29 For equipmem located in air-conditionedCompaaments, cold-day temperatures should be selected from the methods provided in 1 through 3. Themethod select~d depends on the anlounl of information available. For the ground conditions (non-
Ovrating and Operating). a temPeraWre of -W.C should be used for bath Class I and Cla$s II equipment1. Method 1: If a limited amount of information is available, wch as only the
altitude and Mach number, the compaflment temperature for each of the mission flight phases $hould bewlected from the cool.compartment temperatures in TABLE 30.
2. Melhod 11: If the equipment power dii$ipation and compartment equipmentdensity are known in addilion to altitude and Mach number, the cool- or warm-companmenl temperaturesshould be selected for each of the minion flight pha$es from TABLE 30 as follows:
A. Warm-compartment selechon’ If the equipment power dissipates a highwattage and the companment conta!m many other ●quipment$ tending to impede cooling a!r flow,temperatures should be selected from the warm-companment values
8. Cool-companmem $eIecmon: If the equ, pment power dissipalbon i} m)n, maland the compartment is relatively uncrowded with free, unrestricted airflow, the compa.flment temperatureshould be $eIected from the cool-compartment values.
3. Melhod Ill: When additional thermal and design engineering data are ava,lab!e.the companment cold-day temperature can be calculated for the mflsmon flight pha>es u$ing the follow, ngexoreswon
3.4 I x CWkd + 14.4( 1.8)w X7hn) - u , 1.8. .4 x ‘rk)TfCOmp) =
1. S(UXA+14.4W)
Q(Elec) =
w.
T(in) =
u=
A=
T(rec) =
M=
TA =
AltiWde (1000 ft) Temperature ~C)
o -51
10 -26
20 -43
30 -62
40 -65
50 -73
Electrical load (watts)
Air-conditioned flow rate in:o companment (pounds per m,nule)
Temperature of a,r tlowtng Into companment (“C)
Overall heal transfer coefficient, arittsh thermal units per minute per square fool per
degree Celslu$ (BTU/m, n/h2PC)
Compartment area elpo$ed to ambiem (square feet (hZ))
(1 + 0.18M>)[TA + 273) - 273(”C)
Mach number
Ambtient temperature (“C) al altitude
52
MIL-HDBK-781
56.2.4.2 SUDK.\ementallV cooled equinmenl. Supplementally cooled eautpment fol hot daycompanmenl temperature and cold-oay companmem temperaluve should be e$tabh$hed in accordancewith 56.2.4.1, The flow rate. temperature, and dewpoint Iemperalure of the supplemental air should beselected in accordance with the equipment specification during ●ll pha$e$ of the mission profile whichrequire equipment operation, During the ground nonoperating pha$as, the wpplemenlal air flow $houldbe zero. During chamber air heatup. the mass flow of wPPlemenlal air shOuld be the minimum $pecifled tinthe equipment speci Iication and thts should be maintained WXil chamber air cool down. During chamber atr(001 down, the ma$s flow of supplemental air should be the maximum specified in the equipmentspecification and this should be maintained until chamber air heatup.
5.6.2.4.3 Temperature rate of ~hanae. A temperature rate of change should be calculated for eachmission phase which involves a change in altitude or Mach number. This $hOukJ be accomplished bycalculating the compartment temperalur~ of the steady-state condition$ bounding the pha%e in whichaltitude or Mach number varied. calculating the temperature difference of the bounding phase~, and thend,.iding this value by the duration of the varying aftitude or Mach number phaaa. (n the ●xampfe pre$emedin TABLE 25, takeoff and climb to altitude have &cncon\idered a$ a jingle phase from a thermal point ofview. In cefiain cases, two con$ecuiive mis$ion phaaes may involve $uch changw as a dive followed by acl, mb or a loiter condition followed by a dash. In such situations, a temperature rate of change should becalculated for each of the two phase$ The example provided below illustrate$ the procedure:
EaamDle of temoe rature rate of chanae calculation
An aircraft In a cruising mode suddenly climbc. then dives, and finally resumes cruimng FIGuRE 63shows this action. The Iollow-, ng tabulation lists the phases and accompanying data:
Duranon* (C!@!@ Mach Number Altitude (oa r 1000 ft) Compartment 1~~
Cruise 11.3 0.B5 1 1.5
Chmb 1.0 0.75 lt08 3.0
Dove 5.0 0.80 8101 13.0
Cruise 10.7 0.85 1 1.5
Thermal rate! of change are calculated as follows:
CLIMB (cold dav. cool comDanment)
Temperature . +3”Cat8000 fcand Mach Number = 0.75
Temperature . . 1.5”Cat 1000 fiancf Mach Number = 0.85
~atc= 3“C-I.5°C= 1.5”Cpcrminuce
1.0 minuti
f21VE (cold day, cool companmem}
Temperature = + 13”Cat8000 fland Mach Number = 0.80
Temperature = + l.YCat 1000 fKand Mach Number = 0.85
“C Der minute
1.S (use 5)
2.3 (IMe S)
If”l,, =13”C - 1.5°C
= 2.3 CCpermi4uk5.(J minutes
53
------ -.= K-- . . . . . . .
MIL-HDBK-781
S.6.2.5 Vibrat#on. The random vibration level should be determined for each Of the mtSSOOnpha\e$using the information in TABLE 24 and FIGuRES 64 and 65. Special. ca$e vibration dala isco”lal”ed ,n
TABLE 31. Select a value of dynam!c pres$ure (q) from FIGuRE 64 for each steady .state condition as a
function of Mach number and altitude. For lransienl conditions such as dive, the (q) value should be
determined u$ing the Mach numbw for that pha$e, if known, ●nd the average altitude for that phase. If theMach number is not known. the (q] value should be computed a! Ihe arithmetical average of the (q) at the
fta.rt of a dive plus that at the termination of the dive:
ti.tnrt + qtermirwtio.)
2= q aucmgt
If the altitude and Mach number combination is such that the value of (q) isle$~ than 76, uae q = 76, The PSD
(We) should then ba compuled in ●ccordance with the requirement! of TABLE 31. FIGu RE 64 should then beemployed to determine the spectrum shapa (test ●nvelope) and a (W, ) calculated if raquimcf.
5.6.2.6 Humidity Humidity should be injected into the lest chamber and a dewpoint temperature
of + 31°C or greater should be maoncained during the innial pc.nion of the ground, nonoperating phase f.ma hot day. This level of dewpoim should be maintained and controlled until the end of the ground,
0Fra:#n9 pha* fOr a hOt day. NO funher iniecli On of moisture is requt red for any of the other profilepha$as and the humidity during these phases should be uncontrolled. The dewpoinl temperature should bemaintained and controlled al 3 l°C or greater for each wb%equem cycle during the hoi-oay ground.nonoperating and operating conditions Chamber air should not be dried at any time during a Iest cycle RH
should be controlled to ? S percent RH
5.6.2.7 Eauiomenl operatmn. The eq”,pmen! should be in an opetaling mode during all phases of atest profile except for the ground. nonoperating pha!e;
5.62.8 Electrical stress Input voltage should be maintained at 110 percent of nominal for the first
tesl cycle, at the nominal value for the second te$l cycle, and at 90 percent of the nominal for the third te$t
cycle. This sequence should be repeated conunuoudy during subsequent cycles thrOughoul the test The
equipment should be turned ON and OFF at least twice before power is applied conttnuoudy to tieterminestafiup ability at the extremes of the thermal cycle
5.6.3 Construction of an environmental oroi,le See FIGuRE 66. which presents the enviromnenlalpro ftile rewlung from the data entered an the example (see TABLE 24), was detlved from the m,s%ion prof$le
pre!enIed in FIGuRE 67. It should be noted thal m the e.ample (see TABLE 25, combat cruiie phaw) a
change in temperature is obtained even though no change in altitude occurs. Thi\ is due to an accelerabonfollowed by a deceleration In this case, no tem~eralure rate of change has been defined since theacceleral,on and deceleral non are extremely cap, d
5.6.4 Test cwofile development. The environmental profile developed in 5.6.3 should now beconverc~ into a test profile which reproduces those phase$ of the envimmmental profile which reflect the
●quipment exposure and wh,ch can be s,mulated in a test facility. When co”vert, ng frown the enviromnentalto the test profile. the ground rules and procedure! In 5,6.4.1 through 5.64.4 should be uwc!.
5.6.4.1 Vibration. A maximum of four vibrat,on level> (WO values) \hould be used in any paniculm
left profile for each of the two mi$\ion$ (cold day and hot day). These leuels should be ●$labl ished using I he
$tep$ specified in a through d (wep$ 1 through 4):
a. Step 1. Review the (Wo) values listed for each phase and delete any levels which are Ies!
than O.001.b S1ep 2. Identify the (Wo) and duraucm assoc~ated with takeoff and apply lhese values 10
the test PrOflle as shown in TABLE 25c. step 3. ldenufy the (Wo) and durations associated with the highest and Iowe%l (q) levels
and apply these val. e%lO1he test pro f,ledurang Ihe pha$ei ,nwh, ch they occurred
I 54
MIL-HDBK.781
d. Step 4. The fourth level of (Wo) is established by calculating a time. weighled average ofthe (WO) values remaining aher ndentiflcalion of the takeoff. minimum, and maztmum Ievel$. This isaccomplished by multiplying each (Wo) by its duraluon, add, ng these products. and then dividing thi$ sum bythe sum of the durat,on$. The resulting fourth level should be applied to those test phases a$soc)aled withthe ●nvironmental profiie phases which were used tocalcuiai~ the fourth le}l level. in each cage the
duration $hould be as \tipulated in TABLE 24 for that particular phase. For ceraain aircrah flying relatively
benign mission$, all or most (WO) values may ba Ias$ than 0.001 gVHz.
A value of W. = 0.001g2 /fiz thould be stipulated for mission flight phases not accounted for by any of thefour (wo) defined in a through d (sleps.1 through 4) abOve.
5.6.4.2 Temperature. (f the temperature rate of change calculated for any transient condition is lessthan 5“c per minute, a value of 50C per minute should be used. Any thermal condition which is less than 10”Cor less than 20 minutes in duration should be deleted from the lest profile.
5.6.4.3 Example of test orofile. FIGURE 66 is the test profile developed from the sample mission andenvironmental! pro f,lei. TABLE 24 Itists in tabular form the actual data used 10 conslrucl the te$t pro ftile.NoIe Ihat the transient thermal condition (-19°C to-10”C for a period of 5 minutes) was deleted from thetest profile. All values o! temperature rate of change which were less that 5°C per minute were changedalso The durallons of those phaw! were reduced and all other phase durations were maintained a!
originally specifted. Three levels of vibration remained after application of the ground rules: takeoff,mimmum, and maximum. The (Wo) associated with takeoff i$ selected from TABLE 24; a maximum of W. =
0.007 and a minimum of WO = 0.0019 were oblained from thii table atier all values of WO <0.001 wereexclwed Stnce these values and the, r associated durations d,d not acccwm for Ihe lotal mls%,on lime. a Ieuelo’ W. = O.@CI1g> !Hz was specif, ed for ur!accounle.d time peri@d$ {w? TABLE 25!
564.4 Test t)rofiles for variouiaircrafitv cm. unle$~ otherwise specif, ed by the procuring acuvlty.the test profiles shown on FIGuRES 69 through 102 should be used during rel$atml,ly Ies:, ng These pro f#leswere der, ved from the m,ss, on pro f,les in FIGURES 57 through 62 using the method% vn 564 1 Ihrough
56 <.3
5.6.5 Composite envlronmenlal test profile for multimission aDo lica!iom. A compos, te lest profoleshou)d be developed for those simal,omw here it is anticipated that the equipment wil! be u%eo during
more than one lypeo~ mhmon Inlhis case, a Ieslprofile musl redeveloped for each !denl; f,ed rmss, on for
which Temperature, wbralnon. humldtly, and input voilage Ieveis and Ourat tons ha.e been Oelerml neti. Thecorrpos, te lesl p.ofole framework should be structured to retain the concept of two miss, ons in each testcycle. One mis$mn $Iaru from a cold ●nvironment and proceeds to a hot environment: the second slan$from a hot environment and returns 10 a cold ●nwronment. Provisions hawe been Included #n the structurefor exposing the eauipmenl to three temperature levels during each mission and four vibral, oc Ievek during
each test cycle. Thi\ procedure requires thal an environmental test profile for each applicable mission andan estimate of the relat, ve frequency of occurrence of each mission be available m the user.
5.6.S. 1 Reauired in formal, on. A test prof,le for each mission must be developed. Each prof,leshould indicate tempwawre levels and rates of change and their duration for both the hot-day and cold-daymissions. In addiuon. all vibration levels and ‘corresponding durations should be identified. The estimatedrelative frequency of occurrence of each m,ssion should be determined from an an*lySis of the equipment”>
aPP1, caliOn and the hOsl Pla:form. A relative frequency of occurrence is defined M the proportion of thetotal missions contributed by a“ ind, wdual mtssion type. The sum of the miwon weighung factors over all
applicable miwons should equal 1,0.
5.6.5.2 Temperawre The procedures provided in a through d are identical for the hot-say and cold.day m!won% SeDarale analy$as should be performed for each mlmon.
a. A table mmilar to TABLE 32 should be prepared. Each steady +lale temperature level andit$ c.wre$pur, dir, g dtiratmn should be l+$ied for each applicable m,iisier,. The m,issiofi-.weiqh: inrj !ac:w !0:
55
MIL-HDBK-781
I
each JTIIss&on \!m. d be bdenttftecl rhe wetyh ted durat, om should be determined by multiplying earndura!!on by the ,,]rrespond#ng mjss!on.weightmg factor
:, The information prmented in TABLE 32 should be wmmanzed. and a table s,m,lar 10TABLE 33 should bu prepared. Eve,y umque temperature appearing in TABLE 32 should be Io%ted In
ascending order t:) TABLE 33. Only one entry per temperature value should be made an TABLE 33 no matterhow many time> (hat value appears in the $ame or in dufferent mis$iom. The total weighted duration for
each temperature: level ihould be determined by %umming lhe weighted durations for each entry of thattemperature app:. Iring in TABLE 32.
c Three levels of temperature and their duratiomshould ba \elected from those appearingin TABLE 32 (M AA, INT, Ml N). The MAX should be the highe$t temperature value indicated ●nd the MIN thelowest. The tejt duration for ●ach $hotild be the corresponding total-weighted duration. The INT level
should be determined as the timeweighted average of all the temperature values appearing in TABLE 33that have noI baen included in the determination of lhe MAX and MJN levels. The test duration for the INTlevel should be computed as the sum of the total weighled duratiomof thcna temperature values used in
the determinatiot~ nf INT value.
For example, if the ‘Ollowing are given:
Temperature level Total-weighled duration
“c L!?i!U@
20 15
5 10
3 20
INT =(20x15) + (5x IO) + (3x20)
. :.9.1*C15+10+20
Durauon = (corresfmndlng time$)
= 15+10+20
= 45minule5
d. When determimng MAX (or MIN) level, combine all temperature values in TABLE 33within 5°C of the highest (or lowest ) value by the method of time-weighted average. Duration for MAX (orMIN) should be the sum of the corresponding total-weighted durations. If ●ither the MAX or MIN levels donot have a duration of al least 20 m)nutei, determine a new value of MAX or MIN by time weighling withthe r,ext most severe level(5) until a 20-minute duration h achieved by summing the corresponding weighteddurations. If the INT level does not have a durauon of al Iea$l 20 minute%, specify if to be 20 manutes and
subtract one-half the difference between 20 minutes and Ihe INT duration from both the MAX and MIN
duration. If all the temperature levels of TABLE 33 have been e,hau$ted while computing the MAX and MINlevels and the INT level cannot be determined, identify the level with the longest time. Assume that thatlevel is to be the INT level also. Use half the duration for Ihe MAX or MIN level (a~ appropriate) and the
other half as the duralion for INT.
5.6.5.3 Vibration. A table similar to TABLE 34 should be prepared. Each vib,ation level (Wo) and ,ts
corresponding durauon should be Ilsted for each applicable misston The takeoff (TO) vi bralion level for1 minule should be listed separately from a (Wo) of Ihe same numerical value which ij derived by calculation
S!milarly. the (WO) of 0.001g2 IHz and its corresponding duration which has been added 10 requirecormnuous wbrauon (see 5.6.2.5) should be listed separately from a (Wo) of 0,001gl IHz lhat was der~ved by
calculation. These two entnes should precede any other miwon vibration entries. Each miswon’s wetgh~,n~
factor should be identified Weighted durauom should be determined by multiplying each durat,on by Its
56
MIL-HDBK-7R1
I
Corresponding mts%ion weighting factor. The information presen!ed in TABLE 34 should be wmmarczed andatablesimilar lo TAEJLE 35$hould be prepared. The TOand 0.001g2 /Hz levels tdenIif, edin S.6.2.5 and theIota! weighted durat, on should be Itsled $eparately and span from the same values determined bycalculation. All other un, que wbration level~ (Wo) appearing in TABLE 34 should be listed in TABLf 35 tn
a$cending order. Only one entry per (Wo) $hould be made in TABLE 35 irrespective of how many llmes thatvalue appears in the mme or in dtfferem rn,ssiom. The total weighted duration for each (WO) value should
be determined by wmmnng the weighted durations for each entry of that (WCJ in TABLE 3A. A (W.) Of TOfor 1 minute (Iakeoff condttton) should be $elected.The minimum (Wo) of 0.001g> IHz corresponding 10continuous vi b,ation during the fbght phaws$hould be applied for a pariod equal to it! total-weighted
duration. In add,lion, three levels (MA.x, INT. MIN) should be determined for the remaining values providedin TABLE 35. The MAX level should be the highest (Wo) listed and the MIN level $hould be the Iowfit (Wo)lifted. The test duratmn for each should be the corresponding total-weighted duration. The INT levelshould be detemnined as the time weighted average of the remaining (Wo). The test duration for the INTlevel should be the sum of the total we,ghled duration$ of the (WO) u$ed in determining INT.
5.6.5.4 Conslruclion of the composite test orofile. Conslruflion of the composite test profile isprowded jr? 5.6.5.4.1 through 5.6.5.4,5.
5.6,5.4.1 Temperature. One test cycle should consist of Ihe sequence of Ie.el$ specifted in a
through k:
ab
:.
e.f
9h.
1.
J
k.
-54*C (nonoperating)-54’C (operating)INTc (cold day)
MAXC (cold day)
MINc (cold day). 71’C (nonoperating). 71’C (opera l,ng)INTH (hoi day)
MAX” (hot day)MINH (hot day]
Return w -WCC (nonoperating)
The durauon at the two -54’C conditions and the two + 71°C condition% should be 30 minutes each Theduralnon at each of the olhe, levels shoula be determined “sing the procedure in S.6.5.2. The temperature
rate of change between any two levels should be determined by reviewing comparable pha$ei of each!nda., dual lesl profile and selecung Ihe most typical value. The duration of exposure 10 a lemPelalule rdleof change should be determined ~rom:
I>ura inn .cndtempemfure - Nan fcmpemlum
m fe of cha nge
The entire cycle w;{h dwells at all levels and transitions between levels should be listed in a table similar 10TABLE 36.a, dep!cted graph! ca.llyal FIGu8: 103.
5.6.54.2 V! bration. The vibrat:on requiremenl$ should be integrated with the temperaturet,mellne. The MAX vi bratmn level should stafl at the same time as the MAX lerTIperJture levels and COnllnuefor the tame permd determined on 565.3. The MIN vibration level should !lart al the conclusion Of the
exposure to the MAX vibrations levels and continue for the time determined in 5.653. The exposure 10 theINT v,brat, cm level for the time determ, ”ed i“ 5.6.5.3 should start at a time calculated to assure Ihat 11scompletion cm”cide% twth the start of the MAX vibration level. The takeof{ level should be applied fOr 1
minute at theilan of each of Ihewans, tmns from -548C tol NT and from + 71-C 101 NT. A level of (1.001 g2/lizshall beapploed d.rnng all cuber pe, nods, e.cept for the-54’C and . 71°C soaks Thev, bratoon requ:remen,. s
for onecomple:ecyde should be I,sled ana table wmilar to TABLE 360rdepticled graphically a! an FIGuRE103
57
—------- ._. s....-> —. —___ .. ...—.— ------. . . .—------........ .
MIL-HDBK-781
56.54,3 Humid, [y Humid,ly should be injected inlo the test chamber and a dewpo, nttemperature of . 31°c or greater attained during the initial portmn of the ground. nonoper~ling pttiase fora hot day. The dewpoint temperature should be maintained and controlled until the ●nd of the ground,
operating phase for a hol day. No furfher in]ectmn of moisture I> required for any G! the other profnlephases. and the humidity during lhe$e pha$e$ should be uncomrolled. The dewpo,nt Iemperalure \hould bemaintained and controlled at + 31°C or greate, for ●ach subsequent cycle during the hot day ground,nonoperating and operating conditions Chamber air should not be dried at any time during a test cycle
5.6.5.4.4 EauiDment ooeration The ●quipment should be in an operating mode during all phases
of a test profile, except for the ground, ponoperaling phases
5.6.5.4.5 Electrical strefs. The input voltage should be maintained at 110percent of nommal for thefirst test cycle. at the nominal value for the second test cycle. and at 90 percent of the nominal for the thl rd
test cycle. This sequence should be repeated continuous y during wkequent cycles during the lesl. The
equipment should be turned ON and OFF at lea\t lwoce before power i$ applied continuously to determonestartup ability at the enremes of the thermal cycle.
5.6.5.5 Eaample of composite test orof,le This example provide% the procedure for deuelop, ng a
composite environmental tesl prof,le for a Class II equipment that is altached 10 struclurec adjacent 10 the●xternal surface of a jet fighter aircrak. The following data indtcales the mimons in which the equtpment ,>
wad and the relalive frequency of occurrences of each mtwon
Mnn+On tvc.e Relat, ve freauencv of occurrence
LOW-IOW40W 010High-low-low.high 040Low-low-h,gh 025Close wppon 0.20Ferry g
Total 1,00
Since these conditions correspond 10 those of the !ample test pro f,les shown in FIGuRES 69 through 102,
they may be used direc%ly FIGuRES 89 through 93 are corresponding lest profiles for the .miwom
●numerated above. Temperature and vibration levels and cturahom may be read d,recdy from the~e fvgures.-.. ,, .,.lFU?appl(catton or me proceOure ($ Illustrated m the table$ I(st.?d (n a through c:
a. TABLES 37 and 38: hot day temperature
b TABLES 39 and 40: cold daylemperaturec TAB LES41 and 42: v, bration
Rates of change of temperature between levels are determined by reviewini .=.corresponding phasej C.8the individual test profiles and $elect#ng the most appropriate one. The selected rales and calculated
durations are listed in TABLE 43 The completed composite profile is provided in a time!ine in TABLE 44 andshown in FIGURE 104.
S.7 Combined environments for VISTOL ●auiDment. The combined ●nvironments for Type$ A and 0VfiTOL aircraft (see Reference 21) are Spec,f,ed tn a and b:
a. Type A ISa tyin-engtne, subsonic aircrafl de$tgned for sea control and utility missions,including antisubmarine warfare, a,rcrah early warning, tanker ser.ice. ordnance del,.cry, and assault. Th, s
aircrafi can take off and land vemcally O, horizontally,-Venical operatmm are accomplished by a rolal, on of
~
the engtnes.
b Type B i! a twin-engtne. supersonic aircrah wh,ch is apprommately 10,000 pounds ltghler
than the Type A aircrafl The Type F,aircrah ii de$lgned for a f,ghler-a: tack role and can perform !ntefcep~,
58
and surveillance rmss,ons Th, $ a)rcratl al$o can lake off and land in a verucal or conventional mode The
venical mode is accomplished by use of engine exhaust deflectors
5.7.1 MissIon description. The generalized miwlons for the V15TOL aircrafl provided in 5.7.1.1 and
S.7.1.2 represent the current view of the future role envisioned for V/STOL atrcraft. Each mission is describedby spatial aspecl$ required for the development of the environmental test, Aircratl speed and altitudeenroute to the combat area. during combat. and return to the \hip are identified. The missions and thecharacteristics for each type of v/STOL aircraft are provided. Although ●ach type of aircratt can take off andland in a conventional mode, it it aswmed that all Iakeoffs and iandings will be performed vertically. TheVfiTOL mi$sion profiles are prmented graphically in FIGuRES 10S through 114.
5.7.1.1 Tvoe A VfiTOL mi$$ions. Type A V6TOL mi$$iom are defined in a through g:
a. Airborne early warning: Take off vertically, climb to altitude. crui$e out. loiter, andcruise back at high a(!itude, descend, land vertically
b. Antisubmarine warfare: Take off vertically, climb to altitude, cruise out, loiter, deliverordnance, cruise back a! h,gh alt, tude, descend, land vertically
c. Conlacl tinwe$tigatmn: Take off vertically. climb to altitude, dash at low all,lude, loiterand delwet ordnance at iow alhl”de and low speed, cl?mb 10 high altitude, cruise back at high alutude.descend, land venically
d. -Marine assault: Take off vertically, cruise out at aaa level, hover at 3000 fI, crui\e back atsea level, land vertically
e. Surface attach: Take off vertically, climb to altitude, crui$e out at high altitude, Io!terand oel,ve, ordnance a! 20,000 h at low speed. cruise back at high altitude. descend. land vemcally
f. Tanker: Take off vemcally, dimbtoal:i;ude, cruise out at high altitude, Imter at low
speed and low alti!ude m Uan!f.?r fuel. cruiw back at htgh altitude. de$cend, land vemcallyg. Verocal onboard del(.cry: Take off uenically, cl,mb to altitude, cruise al high alt,tude.
de$cend, land vertically
5.7.1.2 Tvpe B vtS?OL mimons. Type B VISTOL m,ssions are defined in a through c:
a. Combat air pa!rol: Take off venically. <limb to attitude, crui$e out and lo(ter at t’trghal:!:ude, engage in combat at high speed and lower altitude. cruise back at high altitude, deicend. land
vertically
b. Deck launched interception: Take off vertically. climb at high speed to all! lude, dash outand ●ngage in combal at high altitude and high speed, cruise back at high altitvde, descend. land vertically
c Subson, c surface surveillance: Take off verc, cally, climb to altitude, cruise out and Imler
at h,gh altitude. engage in combat at intermediate altitude, cruise back at high allitude. descend. landvertically
S.7.2 Thermal stress The procedures of 5.6.2 should be applied. Whenever V/5TOL designs Includecooling systems and techniques ales,gned to maintain cool ambient conditions for eleclrontc hardware, aClass I thermal enwronmem may be uwd.
5.7.3 Vibration stress V#bralion ef(ect$ on equipment for viSTOL aircrah operating on a horizontalfl,ghl mode are sdent,cal 10 those experienced byconvent,onal ftxed-wing aircrafi. For venical fl,ghl modes(takeoff and Iandtng), the vibratmn Ievel$ are signif,ca”;ly different because of ground effecw TABLE (5. ar!
abridged version of TABLE 31, $hould be used for VISTOL: it includes vibration te!t levels (WO) for V/STOipeculiar takeoff and Iandlng cond, t,on$. The takeoff and landing W value$ were calculated in accordancew,th MI L. STD-81O, Method S14 3, Test Procedure 1,Tesl Condmon 1-3.2.5, us, ng VfiTOL engine parameler
information ior both Types A and B vfiTOL aircrafi.
5.7.4 E!eclr,cal %Iress The eleclf,cal *IWM for VISTOL aircraft should beapplled tn the mannerdescribed in 5.628
59
—.. ---. .— -.._ -_
MIL-HDBK-781
3.7.5 [email protected] i+umidity should be ma!nta!ned $n conformance vwth 5.62 b
5.7.6 Eauloment ooeralion The equipment should be tn an opera!tng mode during all phdses of atest profile, except for the ground, nonoperat$ny phases.
S.7.7 Test c.refiles. T.esi profiles for Typat A and B VfiTOI. a!rcrati are prouided in FIGuRES 1 1Sthfough 124.
S..8 Combined environments for Turbomopeller aircrafi wtd helicomer ●auipment. Combinedenvironments for turbopropeller aircre.h and helicopter ●quipment ●re ●s specified in 5.8.1 through S.8.2 .4.
S.8. ! Turbaoro@ler aircrafi environments. Tha ●nvironmental test levels provided herein are
~ppllcable tO ●quipments mounted wi~~n the fu$ela9e of turbopropeller aircrah. The indicated stres>values pre~nted should be u$ed only if actual str~$ levels ●re not specified in contractual document~. and
mission profiles are not provided. Gunfire induced vibration shwld be considered when the ●quipment ismounted in an attack helicopter in which caae, MI L-STD.8 IO, lest Method 514.3, lest Procedure 1,Tat
Condition I-3.2,4 should be consulted
5.8.1.1 Electrical Mreis Input voltage should be maintained at 110 percent of nominal (or the firsl
thermal cycle, al the nominal value for the second thermal cycle, and at 90 percent of nominal for the th, rdthermal cycle. This cycling procedure should be repeated continuously throughout the reliabilitydevelopment test The sequence may be interrupted for repetauon of input voltage conditions related 10 asuspected failure. The ●quipmenl should be turned ON and OFF at Iea$i twice before power i$ appl, edcontinuously to determine $tamup ability al the extreme of Ihe thermal cycle.
5.8.1.2 Vtibral, on The random vibration envelope on FIGURE 125 shodd be UWC. The vi brat,.a”
~hOuid be applied during the Thermal cycle of FIGURE 126 at me ondlcated level% for 12.5 minule$ at start otphase$ B and G and fm 12.5 m,nutes at the start of the m,won o~ective maneuvers during phases C and H
IIf the mtw,on prof,le has no maneuvers, the full vibration level should be applied for 12, S minutes midway
durir,g phases C and H. For the rema,mng portion of the test period. the vibration level should be reduced10 50percent of the Ievelsof FIGuRE 125-
5.8.1.3 Thermal 51ress. The general thermal test prof,le to be wed is shown in FIGuRE 126 Th, sproi,le s,mulates both ccld day and hot day missions, which together form one cycle The thermal cycle Mconlin”ou$ly repealed until the end 0( the test Prior 10 the stan of the first thermal CyCle, or dfh?r $Iorage
al room ambient, the equipment should be allowed m cold foak for 1.5 hours at the low temperature of thewart of the next Ihermal cycle.
5.8 1.4 l+umid, tvstress Humidity $hould be specif, ed to s,mulate the warm, moist almospher, cconditions e$pecl ally prevalent in Iroplcal chmates, Moisture can be ,nduced directly into equipment dur,”gflight fin a hum,d atmosphere. Installed equipment is also subject to condensaldon. freezing, and frosting asa Tewll of Cllmalic Iemperalure humtdlty condition%.
5.8.1.5 Sucwlementallv cooled eauioment. The chamber air humidity should be in accordance w,th5.6.2.6. The supplemental cooltng a!r may be dried so that the dewpoint temperature is from 3°C to 13°Cbelow the temperature of the supplemental a,r or the chamber air, whichever is lower,
5.8 1.6 Chamber air humidt{y Humidity should be introduced into the Ie$l chamber in phafe D andincreased as the chamber alr temperature increases, keeping Ihe dev.’poinl Ie$s than the chamber air
temperature. The dewpo, nt temperature $hoold be raised to 31aC or greater and maintained and c.amro:!eothrough phases E and F of FIGURE 127. At the end of phase F, “o fwlher injecuon of mo!%lure ISreq~$,ed forthe other profole phase!, and hcjrnidlcy !hall be uncontrolled Th, \ humidity procedure should be repealec!
for each test cycle and phases D. E, and F Orying of chambe, ai, should nol be accomplished al Any I,me
during a:est cycle
60
MIL-HDSK-781
1
I
5.8.2 Helicopter environments. Unless otherwtse specified by the procuring actt.ity, hel#coplerenvironment should be der, ved from MIL.STD-810 and the data Provided in 5.82.1 through S.8 24 Thecombined en.lronments profile i! $hown tn FIGURE 128, and the combined mission profile in FIGuRE 129
5.8.2,1 Electr,ca! sue\! U$e the input voltage variation specified in the individual equipment
specifacat, on. 11Ihe equ, pment speoficat!on does not provide this information, use the following:
W MiJ@ @y
28 VDC 29 22115 vAC, 400 Hz alternating current (AC) 122 104
5,8.2.2 Vibration. Unless olhwwise specified by the procuring activity. vibration test requirementsshould be established in accordance with MIL-STD-81O, Method 514.3. Procedure 1.Test Condition 1-3.2.6. for
●quipment imtalled in rotary wing aircrafi. Vibration cycling from 5 Hz 102000 HZ to 5 Hz for a maximumtime of three hours, using a cycle of 36 minutes on each of three axes is required. Theequipmem should be
exposed to a maximum of 5 g. For equipment imxatled in Army helicopters, the following vibra! ion $houtdbeappl, ed: 0.05 inch (l.27 mm) DA from 5 Hz 1024.5 P.z and 1.5g’$pk from 24. SHzt0500 Hz. The wbralion$hould be applied conlinuoudy from 5 Hz to 500 Hz 105 Hz. The !weep rale $hall be logarithmic and take 15minutes 10 go from 5 Hz 10500 Hz to 5Hz ?hj% sweep $hould be applied once during every hour of
equipment operauon
5.&2.3 Therms! stress Unless othemise !pecified by the procuring activity. the thermal prof,le farhelicopters should be as sDeclf, ed in FIGuRE 128 The equnpmenl also should be subjected 10 e coid \oah at
-62’C and a hoi \oak al + 89C as shown in FIGURE 128
5.82.4 I+umidilf Refer 10 AR7O.3L3 for worldwfde humidtty stress condttiom
59 Comb, ned environment% for a,r.launched weapon! a~d assembled esternal no,e% A method formodehng a,r-Jaunchea weapons and assembled ezlernal slore comb#ned environmenla: stresses where nOfl, ght mehwred dala ,\available(\ee Reference 22) ,$pmwded in 591 through 5.9.3, The test pro f,!e%are to
be tailored from aclual mi%sion-def, ned captive and free. fl,ght environments. The Crater, a for eslablljh,ngthe miwon related env, ronmenlal test pro!iles tnclude time dependent thermal, vibration. and eleclr, ca~stresses w,lh optional humidity and pressure condt!,ons. A general definition of the methodology required
and a de$cr, p:, on of 50W to eslabhch teal)stic environmental lest profile parameters are pro., cleo an 59.2Also, many table$ and f,gures are pro., ded 10 ass!sl in the construction of representative Capl, ve an~ free.
fl,.qt.t envcronmenla! lest cycles A comb, ned environments lesl cycle should be used when Iesl, ng a,r.
launched weapons and a$sembled external stores carried by a,rcrati and helicopter% The equipmentmounted ,rwde these stores s?ouid be tested a%speclf, ed ,n 5.9.1 Ihrough 5.9.3 During the env!ronmenlal
lest cycle, the thermal $Ires%, .ibralion (acousucs), hum,d, ty, and Input voltage imposed on the IeSI ,temshould be varied simultaneously. 5peciftc lesl condl:jons !hould be determined by the type of a,rcrafi uponw!wch the s<.ore IS carried, and it~ mtwrm pro ftle, More% Iog,%tics and late-cycle profile. the equ$pmenl cla~~de$ignalion (see MI L-E-5400). and free-flight envelope (where applicable). 5everal other factors. prowded inde:ail In 59. t through 5.9.3. will ajsi~t in the development of a tesl profde. The overall obje~lve i$ 10evaluate store or mnwle reliability in the test laboratory by simulaung the service use environment%
5.91 Mt$sion grofiles Each aircrah type which carries external store% is de figned to operate wilhln
a specific fl,ghl en.e:ope and fly \pecific caplfve-carry mission pmfales which may include externa! sloleinstallations on ellher lne fuselage o, wing pylon$. wmg ttDs, or both. For store% tesl!ng, the IIighl envelopes
and mission pro fdle%of the hosl aircraft(s) should be determined and used in developing the store capl, ve.carry en., ronmenta! test pro f,les (see TAELE5 66 through 53 and FIGURES 130 through 137). When a slore IS10 be used on more Ihan one aircraft, a percemage dmribul, on by aircrah and m,won should be usec 10
eslabl!$h !he Iett O,oftle$ Whe~ nospec, f:c use ,nforma tion, sava,lable. lhe miss, on.lype d,$tribulnon znTA,5:E .C7maybe tise: Wnendes, g.? Il,gol emelopeja”a I:, ghl m,%~to” pro f(le% are not a.a,lable. Ihe
generalized fl, ghl envelope% in FIGuRES 57 lhrougn62 may be used asa bas,$ fordevelopmenl of lhe
externsl store capl, ve.carry lesl p<ofde$ Each slore. oes, gnaled 10 be launched from a host a,rcraft, IS
61
MIL-HDBK-781
dewgned to fly its own %peciftic free-flight mission profile($). The type($) mission profile(s) for a store tn ltee-flight is e$~entialiy unique 10 its mission durauon, performance, and objectives. Hence. no generalizedprofiles can be provided The composgte mts%ton profile $hould be consistent with the eapected eslremes o’free-flight duration. alutude. speed, and, temperatures An example of the type of tnformalion needed ,s
shown in TALf LES 50and 51 and in FIGURE 147
5.9.2 Environmental test Drofiles. As specified m 5.6.2, the te$l profde should be develooed from theaircraft mission profile. The condit, om which must be defined are Ihe selected climatic categorytemperature, the required operational vibration, humid, ty, and the inpul vollage limits. Each test cycleshould consist of two segments. One segment should stan in the cold ●nvironment category and proceed to
the hot ●nvironment. The sacond segment sfvmdd $tarl m the hot ●nvironment and return to the coldenvironment. Test cvcim exhibiting Ihe$e characteristics are shown in FIGURES 130 and 131 and di$olaved ,n.,. ..–TABLE 46. The mi!sion profile shot..d be analyzed to determine the environmental stress levels encOu&ied
for the mis$ion flight phaw\ (takeoff, climb, combat. landing, and w forth) and the ground conditions. In
addition to the information derived from the mission profile, the data should be compiled a$ specified in athrough d:
a. Equipment class (see MI L-E-5400)
b. Equipment location within the store and the store stationc. Type of cooling for the companmem In which the equipment is located (air-condiuoned
or ram ●ir-cooled)d. Type of ●quipment COO1,n9 (ambient or supplemental air)
A table of environmental profile data should be prepared for the specific aircraft, the stores. and the slores’equipment. Th6 tabulahon should include the information for e through p (in add,tion to the data in the●~ample of 5.9 3):
e.
f.
9h.i.
i.kImn.
0.
P.
Mls\ion phase
Duration (minutes)Altitude (lhousands of h)
Mach number
Companmem temperature ~C)Temperature rate of change ~C per minute)
Dynamic pwcwre (q)(lbtiftJ)PSD, Wo(g~lHz). spectrum maxrmum levelPSD. w, (gllnz), spectrum m,n#mum level
Humbd,ly
Equipment operat, onInput voltage
Sources from which enwronmental data can be obtaaned and the methodology to be used in enter, ng th,$data in the table are d,scusted in 5.9.2.1 through 5.9.2.6.2. The methodology describes how each stress level
should be obtained and prewme$ that no measured data is available. either $pecific or for similar
appllcat, ens. If measured stress level data (%pectftc or wmslar) i$ available, II !hould be used. lest condttiomshould be then developed by applying the vi bralion, thermal, and humidity ground rules discussed in S.9.2. 1
through 5.9.2.6.2. The test environments for the free-flight pha$e simulation are the same as those requiredfor the captive-flight pha$e specified above However, the simulation of free-flight ●nvironment in the test
cycle i$ Itmited to post-launch mis!mn profile testing only (includ, ng the initial captive-flight launchconditions]. Included In this sequence i$ the thermal transition period from one climatic condmon 10 ils
subsequent Cl,matic condiuon (see FIGuRE 131 and TABLE 46). The phasing of the free-f l!ghl test cyclewithin the o.erall reliability test sequence depends on the mis$iles (or store%) projected employment. If a
store is prcqected (by system specift calnon requ!remen:s) IO be launched aher a %peciftc number of Capt, ve.11,ght hours, then the free. fl, ght rel!ab,ltly lest cycle should be sequenced to wmulale the mtwon dural, on
and an equivalent percentage of free. fl, ght launches throughout the overall lest program. There should be
not Ieis than one complete serte~ of free- fl, ght launch te$l Cy<les per tesl item
62
..,, ,,-” ,rnl L-nwvk-78i
I
1.
5.9.2 I Mi%@n chase The $pecific mission phawi shoukl be derived from the mis$ion prof,:e Thenumber. type, and duration of the phase are a funcllon of aircrah Iype. The ground cond{t, ons used for all
externally carried stores and equipment Iype$ should include a nonoperating period followed by a pertod ofoperaliom Slme the equipmenl will often be at eilher a low temperature or a high temperature when in 5
nonoperating mode anti the equipment turn ON wiil occur while the equipment is stili al thal thermal
ccnctitiofi, both hoi end cold t:am shwld be included m :52 :e:t prc!ile. Ea:h ponion of the tes: cycle wi!l
be Composed of appropriate combinations selected from che most applicable of [he therrrial c+te~ardesspecified in a and b:
a. Ground ●nvironmental ●xtreme$ (captive flight- phase$A. D, G, 1, L, O, and Q, and
FIGURE 13U)1. MIL-STO-glc2, Table 520,0.111 II.-, ●Im . . ..+-r- ~fil~ =,~h.phere, end warm m.oi:!,. , .“. ” ...v.p .. ., .”.””. ..”.
atmcr!phere models), or, AR70-38, Cl, asappro!triate2. MIL-STD-81O, Table S03.2.11 (high temperature geographical Climalic categories]
and Table 503.2-111 (low temperature geographical climatic categories), or, AR70-38, C 1, as appropriate3. Selected conditions from MIL.$7D-21O or standard atmOiPhetiC tabie$4. Cktermified by individually ‘eilored life-cycle raqiiiretmenti
,b. Fl!gh! enwronme!?tal c.rtrem?s (captive- and fwe-flighl - phase! B. E. H, !. M, end ?, e!?dFIGuRES 130 AND 131)
1. MIL-STD-81O. Table 520.0-111(hot atmosphere, cold atmosphere, and warm moistatmmphwe model $), or AR70.38, Cl, as appropriate
2. 51ancfara atmospheric tabies (*lancfara, hot. and coio)%!e:ieci .W..uj ... ..l. ,, .,,,, .. . . . ..--A:.;-.-. +.-.-. ... ! cTD.~1~ of $IaG~ard a:m, o@c:;: :.?5!?;3.
~ Determined by individually tailored miwon requirements
The I!r$t half segment of the total test cycle [see FIGURE 130) !Iarts dicer the ambient irans! lion to theground extremes of the specified cold climatic region environment and proceeds through 10 the completionof the seiected hot-c l,mat, c rn,$mo” profiie (phasei A thf6@8 H). The $e<ofid half %I?gmenl bey, f!$ al lhtground ex:re-e$ e! the :pec;f,ed %! :Ii!nsti. .--~fi- =.!’.v!rsm?wn! and returns lhre~gh the re.ma,mng. ..=.-... .cl, mattic phases of the lest cycle to the completion of the $pacif ied ground cold cltmaltc region enutronment(pha$e$ I through Q). A post-test return to ambient occur% after the completion of the last segment of the
scheduled tesi cycles The time of each phase (A through Q) is determined by the re$ult~ Of :he operationalf,eld use study and mission profile(s) requ, remenl.
5.9.2.2 C2uralicn The c!ti:a!icm of each missicm f!igh! sha$e s!ww, ld be ebtained fret!? 1!!? missionprofile, When more specific information is Iack, ng. the external store lest times speofied in a through d can
be u$ed:
a. For a typicaf air superiority fighler with an air-m-air caplive-carry weapon mission only. a
W%C51 T,iisiorl :ime ShGuld be a minirntim, of ; F,Gw, 40 rrimd;~,.b. For a typicaJ tactical or attack aircrafi {ir!le~d;c!ion air<rafl) with an emwnal {aplive.<a~ry
weapon $ys!em for an alr-lo-wrf ace mission or b an ai, crafl wilh a supponing electronic warfare mlsslon
(assembled external store), a typical miwon time should be a minimum of 2 hours.c for a typical air-to-air or ai,.to.surface strategic aircraft mission (endurance), the
minimum mi5si0n time snouia be 2Lt hours.~, $e: ~x;e:r,a! ~apti;e.; a;; ie~ ~,;em,>le~ $;c;e; Cr, ;;an\po P, :argo.:ype airc::$. (;peci~!
!n!ssmn). the a%$umed rn!nimu~ mis:ior! time should be 6.5 hour%
5.92.3 Electrical stress When no values are specified by Ihe individual equipment detail
specifhcauon. input voltage shall be maintained al 110 percent of nom, nal for the first test cycle. al Ihenominal value ~or tine second test cycie, anti at 9CIpercent oi nominal ior the thsrd test cycle. Ti-us cyci!ng
proc+aur~ should be rep$zlsd coniinufiusly thrfiugt,cui lhe leii. Howe@r, ihii 5ecjuEfice rniy b-
!nlerrupted for the repetil!on of inpw volteg? cc,nd!!! on: re!a!ed to.? tpecif,c Iallure. ?+ircrafi and store
electrical Interface compat! b,l, !yfhouldbe maonlalned throuqhoullhe les\ cycles Theeampm en! sh6uld be
MI L-HDBK-781
ltir:ted ON a-d OFF at leas~ lwice in each thermal pha~e before continuous power ,s app:led lodelerm, rw
!l=,-. upab,lity at lheealreme~of thethetmal cycle During the nominal input vol(age$equence$, %hoc.l err.interrupt% ( 10 m!cvosecond% @) to 300@ and Ic?ng-term interrupts (20 m$ 10 150 msl In the Power supply$hould be imposed during the odd-numbered test cycles. When the indiwdual equipment speclf, cat, onrequires a smndby operating mode during specifoed operal# onal mii}ions. the Input vollage stress vanat, ons
ipecified herein for Ihe normal equipment operations should be followed.
5.9.2.4 Vibration strew Random .ibralion should be applied Iolhe inlemal aquipmen; item
designated for store in a!rcrafe imtallatiun in accordance with 5.9.2.4.1. and for the air-launched mlsstle andas$embled ●xternal stores, in accordance with 5.9.2.4.2. The random vibration test level for each phase ofthe test cycle should produce the random vibration respon$.m on the te$t item, required by the maximumpredicted environment of FIGuRES 132 through 134 and TABLE 48 (for (g,m~ overall (OVL)) level
adjustments anU FIGURES 135 through 137 and the equations of TA8LE 49. The maximum predictedenvironment is derived from the 95th percentile with SO percent confidence (for a one-sided tolerance Iem, t]using standard statistical analfiis pmcedurei, for the period of maximum overall random wibration levelThe baseline data was derived from a detailed $tudy of 1839 separate flight data meawremem$ When air.
launched mi$siles or a$sembled external stores are to be installed in more than one location on more than
one aircraft, the highest effective random vibration response level of enpowre 10 be encountered by the tes:item during caplive-flight $houlcl be computed for each lest pha5e and should be used throughout the
captive-flight test. The free- fl, ght response from externally applied vibration should be as de f!ned by themission pmflle performance (see 5.9 2)
5.9.2.4.1 Eauipment performance test The Individual equipment test utem[s) should be sub,ec!ed tc,random vi b,atio” excitation on the most wns,live ax, s The PSD loleranc~ of applted vi brat, o~ can beseleaed according to the Random Vi bra\ion TeSI Methods and P,ocedu,e$ paragraph of Method 514 3 O!
MIL-STD.81O, and the weight reduct, on factor of F,gure 514.3.27. The test ,Iem $hould be attached 10 the
vibration ●xciter in accordance wiih the appropriate Tesl Setup paragraph of Melhod 514.3. MIL-STD-81O
Equipment hard-mounled in service use should be hard-mounted to the tesl I,xlure and [email protected] should use service isolators when mounted on the test fixture. If service isolator> cannot be madeavailable during the te~l, isolators wiIh comparable dynamic characteristic~ !hould be provided Theacceleration PSD of applied vi bra\ion (gllli z).as specilted on the te?t f,xture at the lest item mou”t, ngpoints, should produce the random vibrat, on responses calculated in accordance woth 5.9.24. The durauonof each phase of the tests should be dele,mo”t.d I,om the individual mission analy!ej.
5.9,2.4.2 Fully a$wmbled cap:ive-carrv s:o:es performance Ies:. The test item shall be mounted using
a lest $etup simulating the actual mounting impedance. The Individually installed and operationally capab!e
equipment (inside the fully assembled smre) should be mounted in an actual imtallatmn con ftiguratton Therandom vi brat, ot? input levels, tolerances. and Ourauom for lhe fully assembled store should be measuredrespon%e% as specif, ed in 59243. except that the vibration input level adjustment factor> should be rec!ticed
3 dB from the (g, ~$)(OVL) values shown in FIGuRES 132 through 134 and TABLE 48 This reduct, or. is
applicable only 10 Ihe fully a$~emb!ed a,r-launched miwles and assembled external stores.
5.9.2.4.3 General notes General notes which provide guidance for the development of test pro f,les
are provided ,n a through h:
a. Determination of mission profile vibration levels: The vibration response level for eachphase of the profile will be determined from FIGURES 132 through 137 and TABLES 4B and 49 Where no
ipecific mi%s!on profile is available, the procedure of 5.6.2.5 should be used, with the FIGuRES 132 through137 and TABLES 48 and 49 specif, ed above to determine the vibration respon$e Ievek
b. Cargo aircrafl: Unless unusual mission profiles are determined. takeoff and crutseprofiles (vibration respcn$e levels) can be the only required vi bralion Ievel\,
c. Minimum (Wo) lest level: The mtmmum (Wo) vibration response :es: level should be
0.0019 ~lHz. I{ the calculated response test level IS les~ than 0.001 g2Hz. lhe vibrahon response test m,mmum1.3g,mJ (OVL) $pectrum of FIGURES 132 through 137 and TABLES 48 and 49 should t?e u$ed during lhl$
64
MIL-HD’aK-781
I
ponlon of mission pro f,le. This spectrum should produce a minimum vibration response of 0.001 g21Hz. If it
aoes nol. a (Wo) level of 0.091 g?lH? should be usedd. OptIon: The maximum (WOl vibration level determined may be used for the vi brafion
resptinse level throughout the Ie%,. Uowever. this is not recommended since il osan ovenest condll, on
e. Gtmf;re erw; r.wm,ent: The giififi:e ev~i:cm,~sfit i; m; ccjc;itie:eti ifi :h,i :es:, but
should be considered in the ●nvironmental quahflcation te!t. If applicable, use MIL-STD.B1O Method S19.3f. Composite vibration profile: When equipments are to be installed in wrbopropellen
and helicopters (see s. B), and jet aircrah (see 5.6), a composite random spectrum should be generated See hbelow and 5.9.3 for an example of compo$ite spectrum.
g. wmg and fin up and fuselage ●xternal slores: When a store is to be instailed inmultiple locations on an aircrah, a composite vibration respon$.e profile should be used.
h. For umbopropellen and helicopters, the special lransmis$ion drive and low frequencyblade passage excitation forcing funclions calculated by the method in 5.8.2 of Reference 22 (helicopter)and MI L-STD.81O, Method 514.3 (lurbopropellers). $houMJ be super impowd on the acceleration P5Drejpon$e specwa obtained from the use of FIGURES 132 through 137 and TABLES 4Banti 49,
5.9.2.5 Thermal stresse$. The thermal stressec for supplememary cooled ●quipments should bedetermined for each test phase on accordance with 5.9.2.5.1. All other equipments should use 5.9.25.2. Theduration of the ground lest cycles of FIGuRE !30 (pha$a A, D. G. 1.L, O. and Q) should be long enough toreach initial stabil, zallon of temperature in accordance with the stabilization of test equipment (see
MIL-STD-81O, Stabilization of Ten Temperature paragraph).
5.9.2.5.1 SuDplememall V cooled equipments. The flow rate. temperature. and dewpoint
temperature of the supplemental air should be in accordance with the individual equipment %pecif, cationvalues duron? all phases. except the nonoperating poruon% of phases A, O, G, 1.L, O, and Q. During these
poniom of the test phases. the supplemental air flow should be zero. The thermal environment external 10the test item should be on accordance with 5.9.2.5.2. During surrounding external air heal UP. the mass flow
of supplemental air !hould be the msnimum specified, and th, s should be maintained until the mrround, ngexternal air cools down. During surrounding external air cool down. the ma$~ flow of supplemental air
‘f ,+ and !F& $hou!d & m~inlaiged ufllil the surrounding erler”al a,r he?l.$ up:!wx!d be @ -eximwm specl ,e..
5.9.2.5.2 O1hec ecwtpmenls The thermal $trewes in each test phase should be in accordance withFIGURES 130 and 131 and TABLE 46 and the ●nvironmental $tresse$ of the applicable mi~sion prof,le Use the
methods of S.9.2. 1 through 5.9.2.4.3, if a mission profile is not available. An example of the comtruclson of
an enwronmenial stre%s profiie i$ pr~filrd in S.5.3.
59.2.6 Humidi!v strew Humidity should be $pacif ied to $imulate (he warm, moi!t atmosphericconditions especially prevalent in tropical climates. Moisture can be induced direc!ly into equipment during
flight in a humid atmosphere. Installed equipment is subject to conden=tion freezing and f row ng as a
result of climatic conditions. Where applicable, humidily can be varied (from 100 al sea ievel) CL,rectiy withthe sir density ratio, within 25 percem RH.
s.9.2.6. 1 SuPDlementallv cooled eauioment. The chamber air humidity should be in accordancew;lh 5.9.2.6.2. The supplemental cooling air may be dried $cI thal its dewpoim temperature IS from 3-C 1013-C below the temperature of the wpplemenlal air or the surrounding air. whichever is lower.
59.2.6.2 Chamber air humidity, A dewpoint temperature of 31-C or greater should be allainedduring the initial potmon of phase! D. G. 1,and M of FIGURE 130 and maintained unlil the end of these
phases No further injeclion of moisture is required for the other profile pha!es for the fully assembledstores or for hermetically sealed equipment test$. and the humidily should be uncontrolled. For non.hermetically sealed equipment, the RH should vary from 100 percent al sea level directly with the air dens, tyratio (from 9S percent RH 25 percent RH). The dewpo, ”t !emperatu,e should be maintained and controlled
a“. 3 I’C or greater fOr each subsequent Iesl cycle #n Phases D, G, 1,and L. Chamber air should not tIe dr~ed alany umedur;ng a test cycle
65
_ .
I MIL-HDBK-781
5.9.3 Example of conswuctlonof enwironmenlal D~of,le lhlse~ample ,Iluslrates the consuuct, on O( a~o,.>posite mission test cycle profile for An a,rcrafl with a capt$we-(hght aslem bled external sto(e and ,ts
i~ter!mlly inslal led equ, pmenl The example in formauon is as prowded in a through e.
a. Equipment Cla*s 2 in accordance w,th MIL.E.5400b. Equipment installed in air-conditioned mi$\ile or store avmnics compartmentc. Equipment is ambient cooled (no supplemental cooling)d. Equipment is anached to the structure forward of ●tiernal-flow body discontinu,ties The
body contour forward is smooth and free from discon[inuitiea, that i$, no forward control surfaces, antennablades. or blunt noses
e. The final ●nvironmental requirements for thi~example are derived from the data specif,edtn 1 through 20:
1. FIGURE 139, Environmental ●ngineering program whematic.
2. TABLE 50, Preli minary operational d~ign requirements (expected Iif e of S years)
3. FIGURE 140. Logiitic$ functional schemat;c diagram.4, FIGURE 141, European scenario assumed maintenance $chedule and possible operational
utilization rate for environmental analyses (example)5. FIGURE 142. Tacgel movement Vmelme for environmental de%lgn crtteria (European
scenario) - large quantities (e,ampl e).6. FIGURE 143. Estimated percentage of time distribution for transportation. holdldelay,
and handl, ng, for nominal-probable factory-to-theater movemem t,meline.J. TABLE S1, Life cycle enwronmenls
(A) Dislribulion of environmental exposure% and dural,ons.8. FIGuRE 144, Aisumed typical attack aircraft operating envelope (standard day) show, ng
the assumed high-medium-low misuon profile
9. FIGuRE 145. Assumed typical attack a)rcraft operat!ng envelope [standard day ) showtngthe assumed high-low-h,gh mission profile
10. TABLE 52, Assumed typical attack mismzn pro fdles11. TABLE S3, A method for calculahng test prof, !e I!mes for a specific number of test cycles12, FIGURE 146, Vibration factor [g,~$(OVL)]l flight mms, on profile (high-medium-low) use
with FIGuRES 130and 143excepl (“), versus mimmum g,~, (OVL)2(example).
13. FIGuRE 147, V! bratlon faccor [g, mj(0VL)]2 flight mi$tion profile high-low.high use with
FIGuRES 130 and 144 except (“), verws min,mum g,~,(OVL)J (example).
14. TABLE 54, Attach aircrah capuve-carnage mi!iion profile data example
15. FIGuRE 138, Low.low free-f l,ght mis\ion prof!le (example).16. FIGuRE 148, Store free fbghl vibrauon factor (g,m,(OVL)2) flight ml$iion PrOfde 10W.10W
use with FIGURES 131 through 134 and TABLE 48 (example)17. TABLE 55, Assumed free. flighl mission profile for example store (low-low). vibrat, on.18. TABLE 56, Assumed Iree-fl, ght mm%ion prof,le for eaample store (low-low) standard day19. FIGuRE 149, Unil g,m$ (OVL) acceleration P5D ver$u$ frequency spectra (frequenc,e$
should be determined by Method 5143 of MI L-STO-81O, as applicable).20. TABLES 57 through 60, Composite ie$t cycle profile ●xample timeline$.
The event time$ for determining the temperature for ●ach pha$e (prior to the adjustment by the test cycle
time faccor) are given In TABLE 52 The resulting profdes are given m FIGURES 142 and 143. The
temperature rate-of-change for each capl, ve-fllghI temperature step is greater than or equal to 25’C perminute. The rate of altitude change IS approximately sel at 10.000 h per minute. average for capt, ve-fl!ght
(time to climb. dive. idle descent). The alutude and temperature rate$-of-change for each phase of the
example mi~sion are shown in FIGURES 144 and 145 for captive flight. and FIGURE 147 for free-f ltght. Thevibration response condtliom (prior to the adjustment by the cycle time faclor) are calculated for each fllghl
phaw and listed in TABLES S4 and 5S FIGURE 149 show! {he final vibration response !est (ba$eline
conditions) PSO lo beappl, ed for use with the mlssionprofde ., brauonrespome Iaaorsof FIGu RE5 146,147, and 14B. The dewpoint temperature should be ra,$ed to 31”C or greater at the beginning of phase D
The 3 I“C or greater dewpoon: temperature \hould be macn:ained until the completion of phase L. Ground
66
,.
MIL-HDBK-781
1“
I
Operation, Am blenl Day. For the rema,ning pha$e$ of the tesl profile, the humidtty shoulC be controlledw,th the RH stan, ng at 95 percenl ( ? 5 percent RH) at sea level and following as closely a! powble the
derwly rat#o vartiat,on expected with altitude. For repeated profile cycles, the dewpoint should be checkeda~ specif ted herein for pha$e$ A through O. Electrical $Ire$$ should be in accordance with 5.9.3.3 The finallesl cycle times should be ad; usted by lhe test cycle Iome factor from TABLE 53. The final compcwle lest cycleprof,le Iime!ine for the example is given in TABLE 57. For this egample. the cycle M repeated 10 t,mes (6 h!gh-medium-low misions, 4 h,gh.low. hjgh missions. with one simulated launch on each test item. also consistingof 10 test cycles)
5.10 fdis$ile ;ranspofiaiion, ?lafi~!ifia, ar,d ;Io:aoe. The efifi:Gwner, ta! ccr, di:icw 0!
tramportation, handllng. and storage also affect equipment performance and reliability. In order to addressall of these conditions. TABLE 61 has been prepared. Thii table provides a single poinI of reference for allenwronmental conditions which might be ●ncountered a$ a result Of various methods of tran5P0flah on,handling amivit, es, and storage conditions.
5.10.1 Rail tranmon conditions. The test conditions which are to be used to simulate the effects ofvibration, shock, and temperature which rewll from transporting equipment by rail are provided ,n 5 10 1.1through S.10.1.4 (see Re6erence 24). These conditions will always assume that the equipment ,s no:opera,., ng and therefore no equipment operaung parameters or requirements are given
510.1 1 Vi brat, on leninq FIGuRE 150 encomoa%ses the real world vibration cond,:, ons recmnet bythe railroad !ndustry. The three curves shown on FIGuRE 150 (best, worst, and nomtnal) clef, ne me complete
worauon spectra a<$ocia ted wtth rat: transpona! ion. The worst case (curve 1)represents uncush, oned rat!transportation and was developed by de fimng a curve wh!ch envelopes all condnions Th, $ curve wa!
generated by visually drawing a $traigh! line which encomoaf$ed all applicable data points and wa$
tangential 10 lhe maxfmum values obtained. Thi! curve represents data taken from lhe powe. dens, tyve,ws freq”e~cy plots of apprognately selected sources The best case (Curve Ill) represent% data dep, cl, ng
cushn oned rail transpoflauoa. Thts curve is taken d,rectly from ‘An Assessment of Ihe Common CarrierSh, pp, ng Environment”, by Ostrem ant! God\half whtch 8%d,%cus$ed in Reference 2C It ISshown a! a be!t ca~ebecause !T represents the vibrztion ew’!rcmme~t c.f.a twck. trailer moumed en a ra,l {latca~ 9T.em!
transposed #n this manner are cushioned by both the trailer su$pens, on system and the ra,l car wmerwon
system. Thts cushioning effect prowdes the best protection of ecfuipment with respect 10 shock andvibration expected during rail transport. The nominal case (Curve 11)represents the mosl probable profile a!de ftned by general rail transporl conditions. Thts curve wa! defined wi!h the use of the Compuler generated
regre won *fialy\ ii. U$irIg Ihe iame daia poir, is mentioned for Curve :, a piece -.tii;e. leas: square !Ir,aarregression wa$ performed for each of lhe three segments of the curve. The results of the$e analyse~ werecombined to produce the single vibration envelope shown as Curve Il. These three curves may be $eleclwely$pecif,ed for rail conveyance simulauon tests depending on the damage avoidance requirements eilabl!$hedfor the equipment.
5.10.1.2 Shock testinq. The profile given for shock testing represents the worst-case compos, te ofthe $hock force data reported for U.S. Rail Transportation conditions. The profile ●ncompasses leal-worldcondihom and prowdes nominal $hock tesl parameter%.
~ Duration .-
70 g’sRepetition
10m5 Longitudinal Every 3 minute$
These conditions are the recommended shock test parameters
5.10.1.3 Temperature testinq The nominal temperature range to be u$ed in rail transponation
Ie\ting is specified as follows. As indicated, temperature Ievel$ assume a start and end point at roomtemperature (see FIGURE 151)
Starcln.a point
24:C,
Low Doint H,ah 00t1ll
- 32-C 5A5CEnd point
2A:C
67
.- .,.. . . . .
MIL-HDBK-7131
5.10. ,.4 ~esltimel, ne lointegratti reliability testtng ofallof thecritica! characteris!, cs, ates:,..:l, ne i\necessarY FIGURE 151 provides that t,meline requirement. Indicating the schedule relatoonsh, p
b,!tween ,hoch, vibration, and ternperatu, e te~ting for both cold day and hot day. Temperature levels mu~:
berr!aintained butarecritical only from 15minutes prior toandduring shock te$ting. Eqwpmentistobe,-:.moperati”g and packaged forshipmenl during testing.
68
MIL-HDBK.781
6 TEST IN$.TRUMENTATION AND FACILITIES
6. I - The purpo!e of thts $ection is to a!sure Ihat reliability Iem are adequately planned and
lhat properly Cer’uf,ed and calibrated equipment and facihlies are pro.lded and accepled by the procurtngactlvily. prior 10 the $[arl 0{ reliability iesiing.
6.1.1 ~. This section establishes basic requirements forte$t equipment and facilities used in the
performance of reliability tests
6.2 Test facilities and acwa rawk lest iaciiitim and apparatus wad in the performance of reliability
tests should be capable of prowding the test conditions dimmed in thi$ handbook.
6.2.1 Test chambers. Test chamber$ should be capable of maintaining the environmental conditionsof the specified tesl level. That is, a chamber should be capable of:
a. Maintaining the ambient and forced air Iemparaturas at the \pacified temperature level,+ 2-C, during the test. The rate of temperature change of the thermal medium, in both healing and cooling
cycles. should average not Ie$s than 5°C per minute. Chamber and ●quipment cooling air temperatures$ho”!d be monitored cormnuoudy, or periodically. ala monitoring frequency WffiCieOt 10 ensure proper
chamber operation. Means should be provided *.o inlerrupt the programming used in the aulomattc controlof temperature cyclong until the maximum and minimum air temperature requirements are $ausf!ed.Procecuve dewces should be installed m shut off :heequipmem being tesled and Ihe heating source, in the
case of temperature overruns. However, equipment cooling should be maimained to prevent overheating0! I!w equ Ipm.en: under te:;.
b. Ma!ma, ning specif, ed .ibraiion within + 10 percenl for sinusoidal sweep or singlefrequency. For random vi bral, on, the rules specif, ed ,n 1 through 3 apply: (See the Random Vibrai(on Testparagraph of Method 51C.2. MI L-STD-81O).
1. The ?50 of the [I?s[ C-OnIrOi iign~i ik.u:d iWii deti;ate !roI% $p=tifi~d ;?GLJ;:?,=Q;,z$ by
more than:A + 100. -3 Opercent (+ 3dB. -l.5dB)below SOOHz
B. .100, -50 percent(23 dB) between S00Hz102000 Hz
2. De.iaiiom as large as + 300 percent (. 6dB) and -75 percent ( -6 dB) should beallowed over a c“mulau. e bandwidth of 100 Hz maximum. between 500 Hz and 2000 Hz.
3. II ii recommended that the vibration equipment b.? chscked far preper oper~ticc
after each Z4 hours of operahon and that vi bralion be monitored wiCh automatic devices to prevent ovenestcondnuom
6.2.2 Eauipment coolinq Th@equipment should be cooled by meam of it% de$igned-in C001in9
system. When II is not practical to test the equipment and n%cool, ng syslem a! a unit, $imuiatea coolant
condmom and attribute% used should be included in the lest procedures Regardless of the method ofcooling, all equipment should be tested under contractually specified mission and environmental profiles.The coolant attributes should be as \pecified in 6.2.2.1 and 6.2.2.2.
6.2.2.1 Exlernal cooling When there is little or no mixing between the chamber medium and ;hecoolanc such a$, in the cfucted I!qwd, ducced gas, or direct blast gas methods, lhe COOlanl should be:
a. The type to be used operationallyb. P.t I!w maximum wmperatwe .?nd the minimum rate of flow (in accordance with I?PUI
requirements an the individual equ:pment specification), when the chamber temperature is at the highestc. AI the mimmum Iemperalure and the maximum rate of flow when the chamber
lemperawte is a[ its lowest. (When the chamber lemperatule is below the specifoed lower Inm!l {emveraturefor coolfng a,r, and the eQ”, pmenl i$ turned OFF, the cooling arr supply should correspond to cond,lmns
anttcipateci In the equIpiIIen[ ,r,slaiiat,tir, )
69
!
IMIL-HDBK-7B1
6.2.2.2 Internal CooIan! method. When the gas within Ihe chambe: is used as lhe coolant, Itsnould be:
& At a Ie,nperawe which permits the rerju;rad ;ast IW6! in the appriwei ms: ;Facedure :C
b: Wwined
b, At the minimum rate of flow (per coolent input mauirements in tested equipment
6pe.cif ication) when the chamber temperature is ● tha h@hest
c. Al thn maximum rate of flow when the chamber temperature is m the lowest
6.2.4 Calibration and ●ccuracy. The environmental ●nd monitorirta lost facilitim should be in eropa,operati~ condiiicm, as specified i“ MIL. STD45662. All instwmenU ●nd tesl insnumem~lion used in
conducting fin teats sttoula have an accuracy of mr 19881 one.thhf of tit. tniemnce ior tiiw vafiabio to berna~umct.
6.2.5 TestinQ the test facility, The test f aci~nv nhould be tested to etwure that i! is opermino properlyundef the requirad test conditions, Unless otherwise approved by the prdcuring gctivily, equipment other
than the !0s1 samplns should be used 10 vmrify propw Opermion of the 18s1 f?cili.
6.2.6 ifisfdialkm 61 the iw.t kern in lha t.sst factih’f, Ufi;a.. “U ,.s .+I.a .P6., B,.. w .,,. P;G.CW+EZ.- . ---- .:- -- -: *-. . . . . . .
SC!!V!!Y, !!?* WS! i!em s!%w!d Lw in3tMed in the test fc.ci!ity in e menner whkh eimulnws c.wvice uc.ege.
Connections and anached inslrumemation should ba usad only as absolutely necessa~ for the $est. PIIWS,covers, and inspection plates not used in opetation. but used in servicing, should remni. in place, Whnnmechanical or electrical co”nmctiom are not used, the connections normally protected in mwice should be
●dequately covered. For tests in whtch temperature values are controlled, the test chamber ghould be at
standard ●mbient condkions when she t=st imrn is instalied. Tk t.mt item .houid Ihen be oparnted tu. . . ..-. -. . . . . “. -..=. =,,0,14,= ., ,.. , ,V ,.. a:!ur, cti=n 0: eamafic was cr~scd CJe to !Bu!ty ir.:te!!s tic?. C: !uwnd!i.-.~.
6,2.7 Subject term (kevwotd) listing.
Combined environmental tmt conditicmsEnvironmental Stress Screening (ESSI
Envwanmantal tem profiles
i.if6-CYCid environman;si prct;hsMissicn pdi!es
Production ReliabiliIv Accememce Tests (PRATI
Rdiability Development/Gr.awth Tests (RDIGT)
Reliability Oualif,cmion Tests IROTIReliability test methodsadi8biilty test picms
70
MIL-HDBK-781
7 REFERENCES
.,,
1, Duane. J.T. 1964. Learninc Curve AD Woa<h to Reliability Monilorinq, IEEE Transactions on
Aerospace, 2: 536.566
2 Crow. L.H. 1974, Reliab,litv Analwis for Comcdex Repairable Sw:em$, US Army Material SyCtem$Analym ActBv#ty, Techmcal Repon 13S, Abardeen Proving Ground, MD.
3. Ascher, H. E.. 1984, On the Estimation of Reauired Screenina Time to Ensure Zero RemaininqDef~~$ pre~enled at the !n~titute for Environmental Sciences A.mwa! Techrticcd Meeting
4. A. Haner, H, L., 19S4 New Table$ of the lncomDlete Gamma Function Ratio and of PercenlaqgPoint! of the Chi. sauare and Beta D,$tributions, U.S. Government Printing Office, Washington, OC.
5.. NAV:”lAT P-9492. ?W%i :979, N*w-i Mandfacw:iaa X:eenimi mar==.
6. Sexton, T. ,1972, MRI and RAT Evaluation Procedure, Grumman lnIer-Office Memorandum,A S1-340-1.72.264.
7. Schmee. J. and kryant, C M., February i971k, ‘Confidence Limit\ on MT6F for Sequential Test Plansof MIL.5TD.781., Technometric$, Vol. 21, No. 1.
8. Wald, A., 1947. Sequential Analysl$, John Wdey h Sons, New York, NY
9. Epstein, 8. and Sobel. M. 19S5. “Sequential Life Te$ti in the Exponential Case-, Annaf! ofMathemal,cal Sla!,slics, Volume 26, pp. 82.93.
10 Bazof$ky. l., 1963. Reliability Theory and Practice, Prentice Hall.
1 I. Handbook of Mathematical Function! Wjth Formulas. Graphs and Mathematical Tables, U.S.
Depanment of Commerce, National Bureau of Standards, Apphed Mathematics Ser,es. No SS.
12. Butler, D. A.,and Lieberman, G.J., June 1980. An Early. Accepl Modification 10 the Tes! Plan% of-m,c Techn; :a! Eepo~ NC, lg~, Dep~e.ment of Opera!iem Re~eafch mc!M!I/ta~,. S:anda:d .”,
Depanment of Stat, st,cs, Stanford Umversity.
!3. Mann, N R., Grubbs, F.E., 1972. .Approximalely Oplimum Confidence Bound% on Series systemsReliability for Exponent#al T,me to Failure Data-, B,omelrica. VOI.59. PP 191-204.
14. Mann, N. R., 1974. ‘Simplified Expre%$ions for Obtaining Approximately Oplimum SyslemRehabili!y Confidence Bounds from Eaponenttal Subsy$lem Dam.”, Journal of the American
S1atiSt, cal Association
15. Mann. N. R., Schaffer, R.E., Singpumvalla. 1974, Method$ for Statl$l, cal Analvsis of Reltab,lllv andLife Data, Wiley.
16 CORADCOM, February 1979, Product Aswrance and Test Directorate. procedure for Use of
Environmental %of)les in Rel,abihiy Requirements of MIL.STD-781
17. Report Serie%, Annual Repo& 5ep 3:78, Commanding Of f,cer. Naval Ship Weapon System$
Engineering Stat, on, Port Hueneme, C4 93063. Environmental pro f,les for Re!,abiln~ Tesl*nq OfNavv Electronic Equ, omer.I. Annual Repon. December 1978
18 Naval ocean Systems Center, San D8ego, a, t“v,,onm.?nta~ Pro f,les for Enwronmenlal TeSllnO @f
Electron c Eou:Pmenl, March 1979 (wbmar, nes)
71
f .---- c,,, , ,,,,,,
Mli.-t-ff3BK-78:
23
24
Wedpons Qual!ty Eng, veer!ng Center. Naval undef~ea Warfa, e Engtnee,, ng S:al!om Key?o’1. WA.Underwater Veh,cle Environments
RM5-79. R. 1. Development of Fnv, ronmental pro f,le% ior Te%hnQ Eaui Dmenl Installed $n NavalAircrafi [Fizeci ‘W!n~, Grumman Aero$pace Corporahcm, Februa~i 1S79 (A D-AC997 13).
RM5-79.R.3, Develoomenl of Environmental Pro fsles for Teslinq Equipment Installed in NavalV/510L Aircrah , Grumman Aerospace Corpormion, May 1979 (AD-A099744).
3-5631 W4R-238, 28 September 1984. Recommended Reiiabilitv Environmental Stress iesiinqConcfiiions for rielicooler tiounted EauiDm*ni snti &,-*7Meti Ezie:na! Y,cres. LTV Ac:o; pa: e.,4 n. f...c. c..- . . . .“. - -. ...,- -“, ,! F”..,.
Piersol, A. G., December 19B4, Vibration and Acou$tic Teit Criteria for Cdmive Fl,ahl of Externally
Carried Aircrah Stores AFFDL-TR-71-158.
gW ~Wf~L.S?D.7S! Vada:c S.J..,.~~. 0.a,l Trac\~P=~,~~r. f.~. ~.. f.:~;f,’, ~ . D=!?M!cn Envirmmental
- ,5PM Corp0ra18cm
Custodians:Army - CR
Navy - EC
Air FOi-Ct2 - 11
Review ~Ctivi~ieS:
Army - CR, MI, AR, Al’
Navy - AS, SH, OS
Air Force - 01, 10, 13, 16, 17, 18, 19
User activities:
?.rmy - P.T, WC, MENavy -
Air Force -
Preparing Activity
Navy - EC
{Project F.EL1-LX)32)
I 72
a, t,., , ,L, L,, L., L,, ,,- ..-
TABLE 1. Application mg~
MI1-STD.781 Ta!k$ MI1. HDBK-781
Ta$k Number Title Teit Melhod or Te\l Plan Paragraph
202 Reliability DevelopmenIJGrowlh Test Duane Method 4.3,2
(RDIGT)AMSAA Method 4.3.3
301 Reliability Quaflficalion Te\I (ROT) Standard, PtTST 4.6
Slandard, Fixed. Duralion 4.7
302 Production Reliability Acceptance MTBF Amcrance lest 4.5
Te$I (PRAT) Standard, PRST 4.6
Standard, Fixed. Duralion 4.7
Standard. A1l-Equipmenl 4.8
401 [nvircmmentd Strew Xreening (ESS) Computed r5S lime
Intewai Method 4.6.2
Graphical Method 4.4.3
Standard ESS 4.4.4
MIL-HDBK-781
TABLE i. %rnmaryof variables {or lhe AM SAA model
i. x Cumulaove test bme to the ,th failure
2 N Total number of failure! observed
? M N-1
4 1 Total period of observation
5, P Statistic used to tes[ for trend in the data. The discrihudon of p IS in standardizednormal form,
6. ; As,=...,} Pa::me:er e~:imate~.... .WL...C, I-. . . .. .W. .. l-no, ., e ,U,, U,2 :a:ei.:i:h“.-. .-l. ,,-,4 ,,. <Q. ..hm ●ha .,=.i=~.m 6., 6.,,, ..
t.,me If The failure rate ,s ,ncreas, ng, the parameter is geater than ~ne For a
constant failure rale, It is equal to one If the fa,lure rate i$ decreasing (growlh),then tt M less Ihan one
7 E An unb, aseo esumale oi the true vaiue of the growii? parameter
g j. Afier the grow.h Peram,. . .oror estimate ha$ been !i?te!ned, i! is fi._.=.ih!_ IO ~.!tm?.!er---- - .- --1 by i.the$cale paramel. er, . .
9. c; Cramer.von Mises goodness. of-fil test slatl$tic, as calculated from the observat, om
10 ~(~) i,-,terval e;i Im,a;e cf :% $a; !ure rate ,Ii ;he :Ime of ;F,e !.w: !a; !ure
Il. o(t) Interval est, mate of the fatlure rate ala future time
74
..=-. . . . . -.-a. . —— —---—-— ------ .-. -—-. — --- _.___ —_— —
MIL.HDBK-781
I
I
TABLE 3 Summarv O( equatoons. AMSAA model
()
~ x, .;XHN.1 #
8)F-~
i-l
IV- “ ~ -
r
‘t .
XN m
()
g x, .+to
1-1
‘) IJ - N ~
N9)X= —
to ii
‘dikN -~+g[(y+]’10) < 12M
MlnXn . ~ lnXl
1-1
N7) $“
N 1. ta- & in (x,)l-l
TA
BLE
d.E
quat
ion
$ele
ctm
nqu
ide.
AM
SA
Am
odel
.
Equ
ahon
from
7A8L
E3
Par
amet
erT
est
Larg
eS
mal
lS
cale
Par
amet
erG
oodn
ess-
of.
fitch
arac
teris
ticte
rmin
atio
nsa
mpl
esa
mpl
epa
ram
eter
stat
istic
N~2
0N
<20
.
iB
ic;
MT
BF
,@
Con
tinuo
usF
ailu
rete
rmin
ated
3a
56
MT
BF
.(?
Con
tinuo
usT
ime
term
inat
ed7
8
I9
10
prob
ab~
lity
of$u
cce$
sD
i$cr
ete
Fai
lure
onfin
altr
ial
3a
156
%ob
abili
tyof
wcc
eif
Dis
cret
eS
ucce
f~on
final
tria
l?
89
10
I
M~l—
2’
3
4
~
6
7
8
9
10
15
20
30
60
100—
MIL-HDBK-7B1
TABLE 5 Critical va(ues of C; parametric form of the Cramer-von M!ses statistic
0.20
0.138
0.121
0.121
0.121
0.123
0.124
0.124
O.I25
0.125
0.126
9.178
0.128
0.128
0.129
0.15
0.149
0.135
0.136
0.137
0.139
0.140
0.141
0.142
0.142
0.144
0.146
0.146
0.147
0.147
rel of significance t
0.10
0.162
0.154
0.155
0.160
0.162
0.16S
0.165
0.167
0.167
0.169
0.172
0.172
0.173
0.173
0.05
0.17s
0.184
0.191
0.199
0.204
0.208
0.210
0.212
0.212
0.215
0.217
0.218
0.221
0.221
0.01
0.186
0.231
0.279
0,29S
0.307
0.316
0.319
0.323
0.324
0.327
0.333
0.333
0.333
0.336
77
I
I
MI L-HDBK-781
TABLE 6 @fidsnce ,nter.;als for MTB~ fa,lure.tcrm,”aled :e$t
.90 .95 .98
N
2 0.8065 33.76 0.55S2 72.67 0.4099 151.5 0.2944 389.93 .6840 8.927 .5137 14.24 .4054 21.96 .3119 37.604 .6601 5.328 .5174 7.651 .4225 10.65 .3368 15.965 .6568 4.000 .5290 5.424 .4415 7.147 .3603 9.9956 .6600 3.321 .5421 4.339 .4595 5.521 .38!5 7.3887 .6656 2.910 .5548 3.702 .4760 4.595 .4003 5.9638 .6720 2.63d .5668 3.284 .4910 4.002 .4173 5.0749 .6787 2.436 .5780 2.989 .5046 3.589 .4327 4.469
10 .6852 2.287 .5883 2.770 .5171 3.286 .446711
4.032,6915 2.170 .5979 2.6oo .5285 3.05a .4595
123.702
.6975 2.076 .6067 2.464 .5391 2.870 .471213
3.443.7033 1.998 .6150 2.353 .5488 2.721 .4821
1A3.235
.7087 1.933 .6227 2,260 .5579 2,597 .4923
153.064
.7139 1.877 .6299 2.182 .5664 2.493 .501716
2.92 ;.7188 1.829 .6367 2.144 .5743 2.404 .5106
172.800
.7234 1.788 .6431 2.056 .5818 2.327 .5189 2.695la ,7278 1.751 .6491 2.004 .5888 2.259 .526?19 .7320 1.718 .65a7 1.959
?. boa.5954 2.200 .53al
202.524
.7360 1.688 .6601 1.918 .6016 2.147 .5411
212.453
.7398 1.662 .6652 1.881 .6076 2.099 .5478 2.39022 .7434 1.638 .6701 1.848 .6132 2.056 .55A123
2.333
.7469 1.616 .6747 1.818 .6186 2.017 .56012a
2.281.7502 1.596 .6791 1.790 .6237 1.982 .5659 2.235
25 .753d 1.578 .6833 1.765 .6286 1.949 .571426
2.\92,7565 1,561 .6873 J.742 .6333 1,919 .S766
272.153
.7594 l.sas .6912 1.720 .6378 1.892 .581728
2.116.7622 1.530 ,694.9 1.700 .6421 1.866 .5865 2.083
29 ,76a9 1,516 .6985 1,682 .6462 1.aa2 .5912 2.05230 .7676 1.504 .7019 1.664 .6502 1.820 .5957 ~,f)?3
35 .779a 1.450 .7173 1.592 .6681 1.729 .615840
I .905
.7894 1.410 .7303 1.538 .6832 1.660 .6328 1.81645 .7981 1.378 ,7415 1.495 .6962 1.606 .647650
1.747
.8057 1.352 .7513 1,460 .7076 1.562 .6605
60
1.692
.8184 1.312 .7678 1.407 .7267 1.496 .682370
1.607
.8288 1.282 .7811 1.367 .7423 1.447 .700080
1,546
.8375 1.259 .7922 1.337 .7553 1.409 .7148 1.499
I00 .8514 1.225 .8100 1.293 .7759 1.355 .738a 1.431
78
—... — . . . -,, . . ...-=
MIL-HDBK-7B1
TABLC 7. Confidence <ntervals for MTBF, time-terminated Iesl
\
Y
N
-)3a
567
89
1011
1213
la15
1617
18
?9
2021
22232d
2526
2728
29
303540
45
506070
80
00
.80 .90 .95
L u L u L u L
0.261 18.66 0.200 38.66 0.159 78.66 o.12a
.333 6.326 .263 9.736 .217 14.55 ,174
..385 a.2d3 .312 5.947 .262 8.093 .215;,386 ,;52.426
II.i.5i7 .Xx) St%: .2s0
.459 2.915 .385 3.76a .331 .%738 .280
.487 2.616 .412 3.298 .358 4.061 .305
.511 2.407 .436 2.981 .382 3.609 .328
.531 2.254 .457 2.750 ,403 3.285 .349
HE!.E.E!z.E!=.61A.62A
.633
.642
.650
.657
.66A
.670
.676
.682
687
692
697702
.706
.711
.729
.745
.?5s
.769
.787
.801
.813
.831
1.8001.759
1.7231.692
:,6631.630
1.615
1.s941.574
1.557
.545
.556
.565
.575
.~g~
.59 \
.599
.606
.613
.6191.540 .6251,525 .6311,511 .6361.498 .641
L
1.486 .6461.475 .6511.427 .6721.390 .6901.361 ,?~~
1.337 .7181.300 .7391.272 .7561.251 .7691.219 .791
.556
.563
.5701.722 .5761.701 .S821.682 .5881.664 .594
L
1.6A7 .5991.631 .6041.565 .6271.515 .6461.476 ,~~~
1.443 .6761.393 .7001.356 .7181.328 .734
1.286 .758
2.087 .L922.029 .5031.978 .5131.933 .5231.893 .5321.858 .5A01.825 .5401.796
1.7691.745 1
2.3792.3022.235
2.1762.12?
2.076
,438.449.460
,470,479
,488
2.03a‘“”“II‘“.496
1.996 .5041.961 .511
1.929 .5181.900 .5251.873 .531
1.848 .5371.825 .543
1.803 .549
1.783 .544
1.699 .5791.635 .599
1.5S5 .6171.544 .6321.481 .6571.435 .678
1.399 .6951.347 .722
u
1987
24.1011.81
a.0436.2545.2164.5394.064
3.7123.441
3.2263.050
2.9042.7812,675
2.50a2.503~.:~~
2.3692.313
2.261
2.215
2.1732.\342.0982.068
2.035
2.0061.98@
1.870
1.788
1.7231.6711.5911.533
1.488
t .4>3
79
——
-
.—.
_——
——
__——
——
——
==
—.—
..—..—
——
——
—-.
-—.
..-—
.-..—
...—
——
--mu
.-lll%w
eL.,.’-!”*
---------
0m
MIL-HDBK-781
TABLE 9A. [1. Y ) 100 Qercent standard confidence limits on MTBF after accegt decision(lower Ij: ( Y ., ))
LOWER CONFIDENCE LIMITS FOR MTBF 8 ON THE ACCEPTANCE BOUNDARY
TFCTDI AN 1.0 Ii = 1.5 n= R.oln.. ---- ------ —.. ..-— —. ..-
NIJMBER OF TOTAL
FAILURES TEST TIME y = .50 Y = .30 Y= .20 Y= .10
(i)Y= .05
0 6.60 9.521B 5.481B 4.1008 2.8864 2.2031
1 7.B2 4.5976 3.!618 2.5747 1.9807 1.6230
2 9.03 3.3006 2.4386 2.0589 1.6531 1.3957
3 10.2s 2.7074 2.0&13 1.7977 1.4B11 1.2737A 11.46 2.3664 1.8726 1.6387 1.3743 1.1971~ 12.68 2.la52 1.7326 1.5324 1.3022 1.1453
6 13.91 1.9328 1.6337 1.4S69 1,250B 1.1083
7 15.12 1.8785 1.5591 1.3996 1,2117 1.0802
B 16.34 1.7908 1.5014 1.3553 1,1B14 1.05B5
9 17.55 1.7210 1.4S52 1.3197 1.1571 1.0412
iil16,77
i .664S :,4i77 i .29$8 ?.;37: :.0273
11 19.9B 1.6175 1.3864 1.2667 1.1210 1.0158
12 21.20 1.5781 1.3602 1.2465 1.1074 1.0063
13 22.4J \ .5443 1.3376 1.2292 1.0957 .998214 23.63 1.5153 1.31B3 1.2143 1.085B .991315 24.84 1.4839 1.3014 1.2013 1,0772 .985416 26.06 1.467? 1.2866 1.1900 1.0697 .980417 27.29 1.4482 1.2736 1.1B02 1.0632 .9760lB 28. S0 1.4307 1.2620 1.1713 1.0574 .972219 29.72 1.4150 1.2516 1,1635 1.0523 .9688
20 30.93 1.4009 1.2423 1.1564 1,0477 .9658
21 32.15 1.3881 l.233B 1.1500 1.0437 .9532
22 33.36 1.3764 1.2262 1.1442 1,0400 .9608
23 34.58 1.3658 1.2192 1.1390 1.0367 .9588
24 35.79 i.355i ;.2126 1.13:2 7.633? .9%9
25 37.01 1.3472 1.207u 1.1299 1.0310 .9552
26 38.22 1.3390 1.2016 1.1259 1,0285 .953727 39.44 1.3314 1.1987 \.\223 1.0263 .9523
2B 40.67 1.3245 1.1922 1.1190 1.0243 ,9511
29 41.BB 1.3180 1.1881 1.1159 1.0224 .9500
30 43.10 1.3120 1.1842 1.1131 1.0207 .9490
31 44.3 T 1.3064 1.1806 1.1104 1.0192 .9481
32 45.53 1,3012 1.1773 1.1080 1.0177 .947233 46.74 1.2964 1.1741 1.1057 1.0164
II.9465
34 47.96 1.291B 1.1713 1.1036 1.0152 .9A58
35 49.17 1.2876 1.1685 1.1017 1.0141 .9d5236 49.50 1.2797 1.1632 1.0977
37 49.501.0116 .9A37
1,2662 1.1533 1.0899 1.0064 .9404. . ~g,50 ;.2493 ;,; 403
;;
i.0791 ,9987 .935:
49,50 1.2308 1.1254 1.0664 .9B93 .927940 49.50 1.2120 1.1097 1.0526 .9780 .9194
81
MIL-HDBK.781
TAELE9A (1-y) 100 Dercent standard confidence I!mils on ,M~f!er accept Qec, s,on(lower - @[ ( Y , I )] (Cont,nued)
LOWER CONFIDENCE LIMITS FOR MTBF 8 ON THE ACCEPTANCE BOUNDARY
TEST PI AN 11.D d = 1.5. 0=6= 0.20
NuMBER OFFAILURES
(i)
o1
2
3d
5
67
8
9“1o1112
1314
15
16
17
18
TOTALTEST TIME
4,19
5,40
6.627.83
9.0510.26
11.49
12.7113.92
15,1A
16.3517.57
18.78
19.99
21.21
21.90
21.90
21.90
21.90
-f = .50
6.0449
3.12612.3601
2.00771.8069
1.67’68
1.58731.521.91.4718
1.43301.40191.3769
1.3563
1.33921.3249
1.3072
1.2764
1.2420
1.2109
=k-k-k3.4801
2.14771.7401
1.5412
1.4246
1.3478
1.29461,25551.2256
1.20241.1.s391.1691
1.15681.1467
1.13841.1273
1,1059
1,0799
1.0546
2.60341.7675
1.46691.326A1.2432
1.1882
1.15011,1222
1.1009
1.08441.07141,061P
1.05251.0455
1.0398
1.0320
1.0155
.9943
.9727
1.81971.342S1.1746
1.0887
1.0376
1.0039
.9808
.9641
.951s
.9419
.9344
.9286
.9239
.92o1
.9170
.9127
.9023
.8874
.8709
1.39871.0984
.9889
.9326
.8993
.8776
.863 I
.8517
.8A51
.8394
.835:
.8317
.8292
.8271
..925s
.8232
.8169
.8068
.7946
MIL.HDBK-781
TABLE9A ~1- ?’) 100 percent standard con ftdewe I,mit$ on MTBF after accep: dec, %,on(ICWer. e: ( y, I )) (Continued)
LOWE RCONFIDENCE LIMITS FOR MTBF 8 ON THE ACCEPTANCE BOUNDARY
7ESTPLANI II-O d = 2.0. a=B= 0.10r.
UUMBERCIF TOTAL‘AILu RES TEST TIME 7 = .50 -1= .30
(i)Y= .20 Y= .10 Y= .0s
o d.dO . ----0.s4 /9 3.6546 2.7?3$
;.9;09; ,468s
1 5.79 3.336A 2.2913 1.8638 1.4311
2 7.18
1.170A
2.5435 1.8741 1.5790 1.2633
3 8.56
1.0627
2.1789 1.6712 1.4372 1,1783 1.00804 9.96 / ,.9708 1.5521 1.3532 1.1278 .9760
5 11.34 1.8385 1.d754 1.2992 1.0956
6.9559
12.72 1.7466 1.4218 1.261d7
1.0734 .942414.10 1.6799 1.3827 1.2339 1.0575
8.9329
15.49 :,6300 1.353s 1.21359
1.0459 .926216,88 1.5916 1.3311 1.1980 1.0372 .9213
10 18.26 1.5613 1.3135 1.1s58 1.0305 .917711 19.65 1.s371 1.2995 1.1763 1,0254 ,9 I 50
12 20.60 1.5112 1.2839 1.1654 1.0194 .911713 20.60 1.4661 1.2530 1.1410 1.00d5 .902614 ;,417326.66 i.2i63 1.1120 .9835 .mz
15 20.60 1.3755 1.1825 1.0830 .9613 .8715
LOWER CONFIDENCE LIMITS FOR MTEIF 8 ON THE ACCEPTANCE BOUNDARY
TE3T Pi&ii iV. O G = 2.0, G=#?:o.zc
4uMBEROF TOTAL‘AI L(JRE\ TEST TIME r = .50 Y= .30 Y = .20 Y= .10 Y= .05
(i]
o 2.BO 4,0395 2.3256 1.7397 1.2160 .93471 4.!s 2.3277 1.5933 i.2S27
,9=0.6CX2
2 5.58 1.8907 1.3822 1.1581 .9181
3
.7650
6.96 1.6995 1.2865 1.0968 .8869 .74854 8.34 1.977 1.2351 1.0643 .a710 .7407
5 9.74 1.5385 1.2054 1.0459 .86266
,7368
9.74 1.4486 1.1502 1..0066 .64037
.72459.7d 1.3763 1.0986 .9662 .8133 .7069
83
I
MIL-HDBK-781
TABLF 9A ~1. Y) 100 percent stand ar~mence Itmtlson M_T~f:er accepl dec, s!on
iuMBER L)F‘AILURES
(i)
(lower. c?’ ( 1’. t )) (Continued)_.—
LOWER CONFIOENCF LIMITS FOR MTBF 8 ON THE Acceptance BOUNDAR’T
o1
2
34
5
6
TEST I
TOTAL
“TESTTIME
3.755.AO
7.05
8.7010,35
10.3s
10.35
AN v-O d = 3.0. a=~= 0.10
-1 = .50
5.41013.0397
2.4208
2.14621.9966
1.1947
1.6326
Y = .30
3.11472.08311.7755
1.633311.5547
1.4266
!.3112
Y= .20
2.33001.69151.4909
1,39721.3457
1.2S04
1.1575
Y= .10
! .62861.29S01.186!
1.13s7
1.10871.04B;
.9B; I
-r= .05
1.~518
1,0557
.9918
.9633
.9387
.9293
.8600
LOWER CONFIDENCE LIMITS FOR MTBF @ ON THE ACCEPTANCE BOUNDARV
TEST PIANV 1-D d = 3.0, n.8. o.20
NUMEEROF TOTAL
FAILURES TEST TIME Y= .50 Y= .30 Y= .20 -f= .10 Y= .Cs
(1)
o 2.67 3.8520 2.2177 1.6590 1.1596 .8913
1 4.32 2,3418 1.5980 1.2932 .98.?2 .797t
2 4.50 1.63A4 1.2039 1.0142 .BII* ,ljB113
LOWER CONFIDENCE LIMITS FO17MT8F f? ON THE ACCEPTANCE 80u NDARY
TES7 PUN VII-D d = 1.5, a= /3= 0.30
~uMBER OF TOTAL
FAILURES TEST TIME 7 = .50 Y= .30 Y = .20 7= .10(1)
Y= .05
0 3.15 4.5445 2.6163 1.9572 1.3680
1 4.37 2.4854
1.0515
1.7049 1.3856 1.0622
2
.B673
5.5B 1.9410 1.4273 1.2007 .95B0
3
.8035
6.BO 1.6951 1.2959 1.1118 .9077 .7733
4 6.8o 1.4214 1.1207 .9784 .8175 .709?
5 6.80 1.2142 .9756 .B61 1 .7302 ,6L~?
84
MIL-HDBK-781
TABLE 9A. [1. Y ) 100 percent standard confidence limits on MTBF afler acce!m decision
(Iowe: e; ( Y, i )) (Continued)—
LOWER CONFIDENCE LIMITS FOR MTEF @ ON THE ACCEPTANCE BOUNDARY
TEST PLAN VIII-O d = 2.0, a. 8=0.30
NUMBER OF tCJTAL
FAILURES TEsT TIME Y = .50 Y = .30 7= .20 y= .10
(i)Y = .05
0 1.72 2.4S14 1.4286 ! .0687 .7A7L7
1.5742
3.10 1.6120 1.0939 .8814 .6656
2
.S3S24.s0 1.3867 1.0011 .8298 .64s 1 .S268
I
85
MIL-HDBK-781
“TABLE 9B (1 - Y ) 100 percent standard confidence limit~ on MTBF after acce!x decision
(upper. l?: ( Y i)),
UpPER. CONFIDENCE LIM(rSFORMTBF t20NTHE ACCEpTANCEB0UNDARY
- ..-”,..,! . . . . -.a —-. .n,r. >or L.4N l-u u= 1.>. U=p=u. ,v
WIMBER OF TOTAL
‘AILURES TEST TIME y= .50 r= .30 r= .20 Y= .10 Y= .05(i)
rJ 6.60
\
~! ~1 ~, y ~!
1 7.82 9.5218 18.5043 29.5773 62.6420
2 9.03 4.5976128.67112
7.0344 9.;651 ld.5i98
321.7317
io.25 3.3CC6 4.5155 5.7555 0-””Q.”. ! . 10.8:4:
4 11.45 , ::y6: 3.6017 4.~36~ 5.7125 7.2981
s 12,6B 3.0469 3.5B&l 4.5S92
6 I 2.14625.6329
13.91 2.6995 3.1268 3.8772 A.6B06
7 15.12I
1.992B I ~.4623 2.8179 3.4297 4.0699
8 lb.34 1.878S 1.2886 2.5942 ltllm 3,6437
s ;7.55 i .7SG8 2.;567 2.4269 2.875210
3.33i6!E!, ?7 j,?~!o ~,g5~7 .3.2541 ~,~931
11
3.QQ~4
19.98 1.6645 1.9690 2.18B6 2.5482
12 I 1.61752.9043
21.20 1.B99B 2.1017
13
2.4297 2.7517
22.47 1.578’ 1,8420 2,029414
2.3317 2.626223.63 1.5443 1.7927 1.9679 2.24BB 2.520S
IS id. SJ 1.5153 i,7j04 ~, !782 Z,zjcai.9i53
16 25.05% I ::;::
1.2595 2.1159
17 27,29
~.~~:~
1.4482 I 1.6529 I %:
2,0635
18
2.2862
28.50 2.0169 2.2276
19 29.72 1.4307 I 1.6275 1.7630 1.9752 2.1754
20 30.93 1,4150 1.604B 1.7349 1.938! 2.129021 32.15 1.40U9 i.5u43 1.7(IY6 1.904b 2.@373
22 52.36; .3G81
i .S657 i .6668 i .8745 2.CKW~~ 34,53 I ,?7Ga 1.s6s8 1.5659 1.9d7?24
~,fil~g
35.79 1.3658 1.5335;Z; I ::%::
1.9852
25 37.01 1.3561 1.5194
26
1,9571
38.22 1.3472 1.5065 1,6138 I 1.77BB 1.9315
27 39.44 1.3390 1.4945 1.5991 1.7597 1.9079
28 4ij.67 1.3314 1.4636 1.5657 1.7421 I .8863
29 4:.88 1.32C5 1.4735 1.5733 1.7250 1.85.%
30 43.10 1,31813 ! .4641 1.5618 1.7110 1.8482
31 44.31 1.3120 1.45s4 1.5511 1.6971 1.B312
32 45.53 1.3064 I 1.4472 1.5A11 1.6841
33
1.815d46,74 1.3012 :.43:: I 1.5318 1.6721 1.800B
34 47.96 1.2964 1.5231 1.6608 1.7872
35 69. i7 i.2518 1.4259 ;,jijc 1.7745i .6503
36 :9.50 ~,~~~s I
;;:; I ;:r:1.5405 1.7627
37 49.50 1.2?971.3913 I 1.4744
1.62a13 1.7Ad2
38 49.50 1.2662 I.601O
39
1.7177
49.50 1.2493 1.3705 1.4512 1.5746 1.6889
40 49.50 1.230B 1.34B5 1.4272 1.5479 1.6606
1-.— ––. , —.. -— a .-, .— . . . ... . ---- _-. -.. .-a ‘. .,...-.
““0, .”, .m.. -,” ,
M[L-HDBK-781
1
TABLE 9B (1- Y ) 100 percenl standard confidence limits on MTBF after accegt decision
(UOPe- - 6’~. ( Y, I )) (Cont!nued)
uPPER CONFIDENCE LIMITS FOR MTBf e ON THE ACCEPTANCE BOUNDARY
-... 7., A., ,, m 4 —,----- fi, n,,, , .Mn )!. ” “=, . .. U- p-v ..”
NUMBER OF TOTALFAILURES TEST TIME y = .50 Y = .30 -f = .20 Y= .10 y = .05
(,)
o 4.19 ~> ~1 ~t :1 j.
1 5.40 6.0449 I 1.7474 18.7771 39.7682 81.6886
2 6.62 3.1261 4.7865 6.3746 9.8867 14.8006
3 7.83 2.3601 3.3054 4.1254 5.7531 7.75974 9.05 2.0077 2.6766 3.2260 4.2544 5.4393
5 10.26 ! .8069 2.3329 2.7t197 3.5009 4.3300
6 11.49 1.6768 2.1162 2.4SS3 3.0s077 12.71
3.68841.s873 1.9693 2.2S8S 2.7563 3.27B0
8 13.92 1.s218 1.B630 2.117S 2.S491 2.9943
9 15.14 !.4718 1.7827 2.0117 2.3961 2.7881
To 16.35 1.4330 1,7207 1.9307 2.2001 2.6339
11 17.57 1.4019 1.6713 1.8666 2.1895 2.s15012 18.78 1.3769 1.6317 1.8153 2.1179 2,4221
13 19.99 1.3S63 1.5992 1.7735 2.0599 2.348014 21.21 1.3392 1.5722 1.7389 2.0127)5
2,288421.90 1.3249 1.5498 1.7103 1.9739 2.2403
16 21.90 1.3072 1.5233 1.6776 1.931617 21.90 1.276.4 1.4819
2.19011.6293 1.87A3 2.1273
18 21.90 1.2420 1.4391 1.5818 1.B219 2.0764
uPPER CONFIDENCE LIMITS FOR MTBF 8 ON THE ACCEPTANCE BOUNOARY
TEST PLAN II I-O d = 2.0. 0=6.0.10
NuMBER OF T07AL
FAILURES TEST TIME Y = .50 7 = .30(i)
Y = .20 y = .10 7 = .05
0 4.40 ~, ~! ~< ~.
S.79 6.3479 12.3362 19.7182 41.7613
; 7.1885.7~2L3
3.3364 S.1098 6.8060 10.SS7I 1S.8052
3 S.S6 2.S43S 3.563B 4,6489 6.2057 8.3716
4 9.94 2.1789 2.9069 3,5047 4.6238 5.913511.34 1.9708 2.S470 3.0036 3.8270 4.7365
: 12.72 1.838S 2.3236 2.6983 3.3s707 14.10 1.7466 2.1710
4.06412.4928 3.0484 3.6333
8 15.49 1.6799 2.0615 2.3469 2.8333 3.3390
9 16.88 1.6300 1.9802 2.239S 2.677S 3.129510 18.26 1.s916 1.9181 2.1S79 2.560S 2.97S2
11 19,65 1.S613 1.8692 2.0941 2.4709 2.8S8S
12 20.60 1.s371 1.8303 2.0438 2.4009 2.7693
13 20.60 1.s112 1.790s 1.9936 2,3339 2.6873
l’t
~~~~ I ~~~~~
1.7287 1.9206 2.24S3 2.S880
15 1.6671 1.0s1s 2.1682 2.S092
., ,.,he upper I,m(l on .5 IS ,nlnnote, wam zero ODservea rat[ures
87
-——.- . . . . .... .. . .. . .. ..... . .. . . . , ....... .. .. ... .. .... ..... .. . . .. .. . .S-=-.- ”--., ””.>,, ..” .-- .._.
MIL-HDBK-781
TAB I E 9S (1. Y ) 100oercentstandatd confidence Iimits. on MTBF after accept decision
[upper e: [ Y t )) (Conltnued)—
UPPER CONFIDENCE LIMITS FOR MTBF @ ON THEACCEPTANCE BOUNOARY
NUMBER OFFAILURES
(i)
o12
34
5
6f
TEs1
TOTALTEST TIME
2.804.185.58
6.968.3A9,74
9.749.74
AN IV-D d = 2.0. ❑ .B
y = .50
~1
4.03952.32771.8907
1.6995
1.5977
1.53851,4486
-
7 = .30
~1
7.8S033.57322.6681
2.2978
2.1073
1.99831.8613
0.20
7 = .20
~,
12.54804.7640
3.34532.7963
2.5225
2.3693
2.1971
-r = .10
~,
26.575A7.39754.6985
3.7496
3.3033
3.06522.83B7
UPPER CONFIDENCE LIMITS FOR MTBF @ ON THE ACCEPTANCE BOUNDARY
TEST PIAN V.D d = 3.0, Il=@=o.lo
Y = .05
~54.589111.0s317
6.3B3B4.8B58
4.2253
3.S936
3.6262
i NUMEEROF I TOTAL I I I I I:AILURE5
(i)
o11
34
5
6
TEST TIME I 7=.50
i
-i = .30 I r=.20 I y=.10 Iy=.05
.
5.40 5.4101 10.5138 16,8053 35.59207.05
73.1104
3.0397 4.662S 6.2143 9.6459 14,4469
8.70 2.4208 3.4052 4.2604 5.962510.35 2.1462
8.0694
2.8849 3.4956 4,6508 6.003810.35 1.9966 2.6113 3.1057 4.0178
10.35 1,7947 2,3001
5.0622
2.7039 3.4489 4.3109
UpPER CONFIDENCE LIMITS FOR MTBF c? ON THE ACCEPTANCE BOUNDARY
TE5T PLAN VI-O d = 3.0, n= B=o.20
I NuMBEROF TOTALFAILURES TEST TIME Y = .50 Y = .30
(i)Y= .20 y= ,10 y = .05
0 2.67 ~: ~1 ~! 1 ~
4.32 3.B520 7.4858;
1 I .96544.50 2.3418
2~.3A153.6027
52,05464.BOBO 7.a730 11,2010
~lThe upper I!rn,l on 6 IS ,nfinlte, w,!h zero observed fall Ure$
88
.—..— . ...-—
TABLE 98
MIL-HDBK-781
(1. Y ) 100 percen! $tandard confidence Iimil$ on MTBF afler acce!m decision
(upper. 8 b ( Y i H. (Con~,wed)
UPPER CC)NFIDENCE LIMITS FOR MTBF @ ON THE ACCEPTANCE BOUNDARY
TEST PLAN VII-D d= 1.5, a= B =0.30
NUMBEROF TOTALFAILURES TEST TIME y = .50 y = .30 7 = .20 y= .io
(i)
y = .05
n 3.1S ~1 ~, ~1 ~, ~1
1 4.37 4.5445 8.8316 14.1165 19.8973
261.4127
5.58 2.4854 3.8096 5.0760 7.8765 11.79453 6.80 1.9410 2.7236 3.4022 4.749! 6.40954 6,80 1.6951 2.2673 2.7375 3.6186 4.6358
5 . “n 1.22; e
I I i 1“E373
0.0” 2.16% ?.?706 3.eG23
UPPER CONFIDENCE LIMITS FOR MTBF 8 ON THE ACCEPTANCE BOUNDARY’
TEST PLAN VIII. D d= 2.0, a=~=O.30
P
NUMBER OF TOTAL
FAILuRES TEST TIME y = .50 -r = .30 y = .20 Y = ,10(i)
y = .05
0 1.72 ~ ~i ~( 1.
} 3,10 2.cg!4 .?.8223 7.7oe@ ~~,~~49 33.53?32 4.50 1.6120 2.4S94 3.3277 5.1 BI1 7.7733
1, The upper I,m, t on 8 ,5 infinite, ..wth zero observed faihre~
89
I
I
MIL-HDBK-781
TABLE 10A il. ‘Y) 100 Dercenl%ta~d confidence Iimitson MTBF aflgr reiectdecmon
(lower- (7( ( Y ,t))
LOWER CONFIDENCE LIMITS FOR MTBF @ ON THE REJEcTION BOUNDAK?
T.. TD, .S., ,.II A - 1 < “.n-ntn!L.. lr-!. !-w “ - . . . . -- r--- ,-
UUMBER OF TOTAL
‘AI LURES TEST TIME Y = .50 Y = .30 r = .20 Y = .10
(1)
Y = .05
6 .68 .1199 .0971 .0860 .0733
7 1.B9 .2835 .2331.0647
.2083 .1795 .1596
8 3.11 .4072 .3389 .3049 .2849 .2371
9 4.32 .5031 .4228 .382a .3346 .301010 5,54 .5B15 .4926 .4476 .3939 .355911 6.75 .6454 .5505 .5021 .4441 ,402B
12 7.97 .6997 .6004 .5495 .Ua81 .4443
13 9.18 .7453 .6430 .S902 .5264 .4B0614 10,40 .7B52 .6806 .6265 .5606 .513215 11.61 .8194 .7134 .6582 .5909 .5422
16 12.B3 .8499 .7428 .6868 .6184 .56B717 14.06 .8773 .7695 .7129 .6436 .593218 15.27 .9012 .7929 7360 I .6B60 .6150
19 16.49 .9228 .8143 .7572 .6867 .6352
20 17.70 .9420 .8336 .7763 .7055 .6537
21 1B,92 .9596 .B513 .7940 .7230 .6709
22 20.13 .9754 .8674 .8101 .7390 .686723 21.35 .9901 .8824 .8251 .7540 .7016
24 22,56 1.0033 .8960 .B389 .7678 .7153
25 23,78 l.c. .9088 .8518 .7808 .7282
26 24,99 1. : .9205 .8637 .7928 .7402
27 26.21 1.C,,74 .9315 .8749 .8041 .7516
2B 27.44 1.oLt73 .9420 .8855 .8149 .7624
29 28.65 1.0562 .9515 .8952 ,824B .7723
30 29.B5 1.06A4 .9602 .9042 .8339 .7B15
31 31.08 1.0723 .9686 .9 IZ9 .8428 .7905
32 32.30 1.0797 .9765 .9210 .8511 .798B
33 33.51 1.0864 .9838 .9285 .B588 .806634 34.73 1.0928 .9908 .9357 .8662 .8141
35 35.94 1.0987 .9972 .9423 .8731 .8210
36 37.16 1.1044 1.0034 .94B7 .B796 .8276
37 38.37 1.1096 1.0091 .9546 .8858 .8338
38 39.59 1.1145 1.0145 .9603 .8916 .B3’97
39 40.82 1.1193 1.0198 .9658 .8973 .8c54
40 42.03 1.1236 1.0246 .9708 .9025 .850641 43,10 1.1269 1.02B3 .9746 .9064 .854641 44.31 1.1369 1.0388 .9853 .9170 .864941 45.53 1.1517 1.0536 .9998 .9308 .B779@,l 46.74 1.1691 1.0703 1.0159 ,9457 .B914
41 47.96 1.1880 1.08B0 1.0325 .9607 .9047
41 49.17 1.2069 1.1051 1.04B4 ,9745 .9165
41 49.50 1.2120 1.1097 1.0526 .97B0 .9194
90
I
. . . . . . .
MIL-HD81(-781
TABLE 10A. (1. 7 ) 100 oercent standard confidence limits cm MTBF aher reiect decision(lower e! ( Y I )) (Continued)
LOWE RCONFIDENCE LIMITS FOR MTBF @ ON THE REJECTION BOUNDARY
TF$T PLAN II-D d = 1.5. m=a=o.lo.- . . .. —- ..-, . -.
NUMBER OF TOTAL
FAILURES TEST TIME Y = .s0 Y = .30 r = .20 y= .!0 y =.05
(1)
3 .24 .0B98 .0664 .0561 .0451 .03B 14 1.46 .39B 1 .3069 .2649 .21 B7
5
.18&l
2.67 .5B31 .4605 .4028 .3380 .2947
6 3.90 .7133 .s733 .5063 .4299
7.37B2
5.12 .B07S .6577 .5851 .501s .444d
8 6.33 .8783 .7231 .6472 .5590 .49B3
9 7.55 .9347 .776S .6985 .607310
.s440
B.76 .9794 .8198 .7406 .6474 .582A11 9.9B 1.0165 .B564 .7765 .6B21 .615812 11.19 1.0468 .8B69 .B067 .7)14 .6442
13 12.41 1.0725 .9131 .B328 .7370 .669 !
14 13.62 1.093B .93s2 .8s49 .7s.S8 .6903
15 14.84 1.1122 .9544 .B743 .7780 .7090
16 16,05 1.1277 .9708 .89o9 .79a4 .7269
17 17.2B 1.1413 .9BS4 .9056 .8090 .7390
lB 18,S0 1.1s30 .9980 .9184 .8216 .7s1 1
19 lB.78 1.1536 .9986 .9191 .8223 .7s19
19 19,99 1.167S 1.013s .9340 .B36B .7654
19 21.21 1.1937 1.03B9 .9s82 .B586 .7844
19 21.90 1.2109 1.0546 .972? .8709 .7946
91
,-
I
I
MIL-HDBK-7B1
TABLE fi2A. f 1. Y) 100 oercent standard confidence limits on MTBF after reiect dec;s; on(lower (): ( Y .~ (Conunued)
LOWE RCUNFIDENCL LIMITS FOR MTBF 8 ON THE REJECTION BOUNDARY
TEST PLAN III-D d = 2.0. 0=6=0.10-. -.
NUMBER CIF TOTAL
FAILuRES TEST TIME Y = .50 ,Y= .30 Y = .20 Y = .10 7 = .05(t)
3 .70 .2618 .1936 .1636 .1315 .11124 2.08 .572.4 .4403 .3798 .3131 .26965 3.48 .7696 .6062 .S296 .4437 .3B6S6 4.40 .8403 .6700 .589A .4983 .4371
6 4.86 .9027 .7232 .6377 .5405 .4751
7 5.79 .9535 .7708 .6832 .5830 .51517 6.24 .9998 .8117 .7210 .6169 .5460
8 7.1 B I .0383 .8488 .7570 .6512 .57888 7.63 1.0746 .8818 .7a80 .6795 .60509 8.56 1.1037 .9107 .8164 .7069 .63159 9.02 1.1332 .9382 .8425 .7312 .6541
I@ 9.94 1.1556 .9610 .8652 .753.4 .675810 10.40 1.1793 .9B36 .W70 .7738 .695111 11.34 1.1980 i 0029 .9063 .7930 .7138
11 I 1.79 1.2170 1.0214 .9244 .B1OO ,730012 12.72 1.2319 1.0371 .9402 .B258 .745412 13.1 B 1.2479 1.0530 .9s57 .8406 .7595
13 14.10 1.2599 1.0657 .9687 .B536 .772213 14.56 1.273\ 1.0790 .9818 .8661 .784 I
14 15.49 1.2B3 1 1.0899 .9929 .8772 .795014 15,94 1.2939 1.1009 1.0038 .8877 .804915 16.8B 1,3025 1.1102 1.0133 .8973 .8142
15 17.34 1.3118 1.1199 1.0229 .9064 .822716 18.26 1.3187 1.1275 1.0307 ,9142 .830316 19.65 1.3484 1.1S72 1.0595 .9409 .8543
16 20.60 1.3755 1.1825 1.0830 .9613 .8715
92
.
MIL-HDBK.781
(1. Y ) 100 percent standard confidence limits on MTBF af’ler reiecl decision
(lower. c7~( Y , t )). (Com!nued)
TABLE 10A.
LOWE RCONFIDENCE LIMITS FOR MTEF t? ONTHEREJECT1ONB OUNOAR%
LAN IV-D d = 2.0, a= B = 0.20I I I
TEST
TOTAL
TEST TIME
(t)
NuMBER OFFAILURES Y = .50 I Y=.30 I v=.20 I y=.10 Y = .05
.4171
.8127
.8914;.62841.07341.16341,1910
.2870 I .2338 I .1800
.5944 .4997 .3996.1476.3367.3898..4646.5004.5567.5809.6192,~~~j
.6612
.6717,7069
2344s566778B
.702.082.80. . .>.JIo4.184.865.586.246.967.62
.6843 .5646 .4578
.7767 .66.44 .5e28
.B193 .7052 .5809
.8977 .7768 .6438
.9251 .8036 .66931.247B I .976:1.2s54 .~~~ :;;: I :;;;:!.3031 1.0301 .9026 .75861,3147 1.0423 .9146 .77001.3763 1.0986 .9662 .8133
8.349.7A
= 0,10
r = .20
TEST PLAN v.D d = 3.0, a=
Y = .05
.1202
.3564
.5008
.5151
.6200
.6313,7089,7175.7746,8600
NuMBER OFFAILURE5
TOTAL
TE5T TIME
(1)Y =.107 =.50 Y = .30
234A
.57 .3396.8514
1.09931,12751.28161.30071.40301.41641.48661.6326
.2337
.6256
.8334
.85S9
.99321,0094
1.10491.11661.18451.3112
.1904
.5271
.7141
.733B
.8613
.8758
.9664
.97721.04271.1575
.1465
.4225
.5845
.6010
.7156
.7282
.8118
.8213
.8825
.9811
2.223.753.875.405.527.057.17B.70
10.3s
556877
LOWER CONFIDENCE LIMITS FOR MT8F 8 ON THE REJECTION BOUNDARY
TE5T PLAN VI-D d = 3.0, a= /3 = 0.20
NuMBER OF TOTAL
FAILURES TE5T TIME Y = .s0 y = .30 Y = .20 y=.lo Y = .05(t)
2 .36 .2145 .1476 .1202 .0926 .0759
3 2.67 1.0053 ,7422 .6266 .5034 .4253
3 4,32 l,SBO1 1,16AB .9819 .7862 .6618
3 4.50 1.6344 1.2039 1.0142 .8111 .6818
93
~,-,..-.-””. . . . . . . . . . . . . . .. . . . . . . . . . . .
I
MIL-HDBK-781
TABLE1OA [l-y) 100 percent standard confidence limits on MT8F atier reiect decision
(lower 8: ( Y, t )). (Continued)
LOWER CON FIDENCE LIMIT5FORMTBF @ON THE REJECTION BOUNDAR”f
!.. ! r-!. . . ..w “-. . . ,“- ~ - “.. ”
NUMBER OF TOTAL
FAILURES TEsT TIME Y = .50 Y = .30 Y = .20 y =.10 r = .05(t)
3 1.22 .4562 .3374 28s1 .22924
.1938
1.43 .6856 .s245 .4513
5
.3710 .3168
3.1s .7501 .5624 .s0s2 .4199
5
.3638
3.65 .8322 ,6511 .5671 .4735
6
.4115
4.37 .8743 .6908 .60s0
6
.5089 ,4448
SW 1.0323 .8263 .7283 .6172
6
.5421
6.80 1.2142 .9756 .Mll .7302 .6412
LOWER CONFIDENCE LIMITS FOR MTSF 8 ON THE REJECTION BOUNDARY
TEST PLAN VIII.D d = 2.0, a= f3= 0.30
NUMBER OF TOTAL
FAILURES TEST TIME Y = .50 Y = .30 y ..20
(1)Y =.10 Y = .05
3 1,72 .6432 .47s7 .4020
3
.3232 .2732
3.10 1.1121 .8183 .6E8S3
.549a .46054.50 1.3867 1.0011 .8298 .6451 .$.268
94
MIL-HDBK-781
I
I
TABLE 106. [1- Y ) 100 percent standard confidence limit! on MTBF after reiect decision
(upper- 6’: ( Y,t)).
UPPER CONFIDENCE LIMITS FOR MT6F e ON THE REJECTION BOUNDARY
TCc’i’m A., , m A-, .--a-a ,,1,., ! .-1” l-w “-!.>,”- p- ”.,”
4LJMEFR OF TCJT.ALAILLSRES TEST TIME Y = .s0 7 = .30
(t]Y = .20 7= .10 7 = .05
6 .68 .1199 .150s .1742 .2t57
7.2602
1.89 .2835 .3494 .399s .4855 .s7s7
8 3.11 .4072 .4951 .5609 ,672A .7873
9 4.32 .5031 .6052 .6807 .8074 .936510 5.5A .5815 .6933 .7751 .9114 1.0488
11 6.75 .6454 .7636 .8496 .9917 1.133912 7.97 .6997 .8224 .9111 1.0567 1.2015
13 9.18 .7453 .8711 .9614 1.1090 1.255014 10.40 .?852 .9129 1.0042 1.1528 1.299115 11.61 ,8194 .9484 1.0402 1.1s90 1.335016 12.83 .8499 .9796 1.0716 1.2201 1.365417 14.06 .8773 1.0073 1.0992 1.2472 1.391si~ i5.27 .90 i 2 ;.G311 1.1228 : .2?C$ :.2!3219 16,49 .9228 1.0525 1.1438 1.2900 1,4320
20 17.70 ,9420 1.0713 1.1621 I .3073 I .4480
21 18.92 .9596 1.0884 1.1786 1.3227 1.4621
22 20.13 .9754 1.1036 1.1932 1.3361 1.4742
23 21.35 ,9901 1.1176 1.2065 1.3d82 1.4850
24 22.56 1.0033 1.1301 1.2184 1.3589 1.4944
2s 23.78 1.0157 1.1416 1.2293 1.3686 1.5029
26 24.99 1.0269 1.1521 1.2391 1.3772 1.5103
27 26.2 ! 1.0374 1.1617 1.2481 1.3851
28
1.5170
27.44 1.0473 1.1708 1.2565 1,3923
29
1.5231
28.65 1,0562 1.1790 1.2640 1.3988 1.528S
30 29.85 1,0644 1.1863 1.2708 1.4045 1.5332
31 31.08 1,0723 1.1934 1.2772 1.4099
52
1.5376
32,30 ;,G797 i .2006 i .2831 ;,41$3 1.54!5
33 33.51 1.0864 1.2060 1.2886
34
1,4193 1.5451
34.73 1.0928 1.2116 1.2936 1,4234 1.5a4
35 35.94 1.0987 1.2168
361.2982 1.4271
37.16 1.1044
1.5513
1.2217 1.3026 1.4306
37 38.37
1.5540
1.1096 1.2262 1.3066 1.4338 1.5s64
38 39.59 1.114s i .23135 1.3103 1,4367 1.5566
39 40.82 1,! 193 1.234S 1.3139 1,4395 1.5607
40 42.03 1.1236 I .2382 1.3172 1.4420 1.562541 43.10 1.1269 1.2410 1.3195 1.4438 1.563841 44.31 1.1369 1.2500 1.3277 1.4505 1.569041 45.53 1.1517 1.2642 1.3410 1.4621 1.578641 46,74 1.1691 1.2816 1,3580 1.4777 1.592241 47.96 1,1880 1.3011 1.3776 1.4965 1,6o9541 49.17 1,2069 1.3213 1.3982 1.5170<i 49.50 i,2:20
1.6291
i .3268 1.4038 1.522~ ! 3.347
95
MIL-HDBK781
lABLE 10B (1- 7 ) 100 percent Qandard confidence Itim,ls O“ MTBF afTW ,eiec[ decis, on
(upper . e:, ( Y, t )) (Continued)
UPPER CONFIDENCE LIMIT$ FOR MTBF 8 ON THE REJECTION 80uNOARY
TEST PLAN II-D d= 1.5, m=~= 0.20
1NUMBER OF
rAILURES
34
15
67
8
910
1112
13)4
15i6)7
i ;:
L191919
TOTAL
TEST TIME
(t)
.241,46
2,67
3.905.12
6.337.55
8.76
9.9011.19
12.41
13.62
14,04
16.0517,28
18.50
18.78
19.99
21.21
21,90
.0898
.3981
.5831
.7133
.8075
.8783
.9347
.97941.01651.0468
1.0725
1.0938
1.11221.12771.1413
1.1530
1.1536
1.1675
1.1937
1.2109
7 = .30
.1254
.5291
.7s37
.9040
1.00811.0837
1.1420
1.1669
1.22321.25221.27621.2958
1.3123
1.32601.3379
1.3479
1.3483
1.3604
1.38541.4029
I
Y = .20
.1563
.6369
.89021.05381.16381.2415
1.30001.34421.37921.40661,4289
1.4468
1.4617
1.47381.4842
1.492B
1.4932
1.5035
1.5266
1.5436
v = .10
.2178
.83891.13941.32241.4395
1.5186
1.57581.6174
1.64921.6732
1.6922
1.7070
1.71881.72821.7360
1.7422
1.7425
1.7499
1.7686
1.7833
.29351.0720
1.41851.61791.73921.8173
1.8715
1.9093
1.93701,9572
1.9726
1.9840
1.9929
1.99962,0050
2.0092
2.0093
2.0142
2.0277
2.0392
96
MIL-HDBK-781
I
,
TABLE 10B. jl. Y) 100x rcent standard confidence Iimit$ on h4TBF after reiecl decision
(upper 19[ ( Y, I )). (Continued)
uPPER CONFIDENCE LIMITS FOR MTBF # ON THE REJEmlON BOUNDARY
TEST PIAN III-D d= 2.0. a= 13= 0.10
NuMBER OF TOTAL
FAILURES TEST TIME Y = .50 Y = .30 Y = .20 7=.10 Y = .05
(t)
3 .70 .2618 .3658 .4560 .6352 .8S61
4 2.08 .5724 .7631 .9208 1.21W 1.5650
s 3.48 .7696 .9986 1.1831 1.5226 1.907s
6 4.40 .8403 1.0760 1.2643 1.6079
6 4.86
1.9949
.9027 1.1491 1.3444 1.6982 2.0930
7 5.79 .9535 1.2023 1.3984 1.7519 2.1450
7 6.24 .9998 1.2542 1,4535 1.8106 2.2052
8 ?.18 ~.03a3 1.293 \ 1.49}8 \ .6469 2.2385
8 7.63 1.0746 1.3322 1.5321 1.8878 2.2783
8.56 1.1037 1.3606
:
1.5594 1.9125 2.2999
9.02 1.1332 1.3913 1.5902 1.9423 2.327S
10 9,94 1.1556 1.4125 1.6102 1.9597 2.3419
10 I 0.40 1.1793 1.4364 1.6336 1.9814 2.3610
11 11.34 1.1980 1.4536 1.6495 1.9946 2.3715
11 11.79 1.2170 \.4724 1.6674 2.0106 2.3849
12 12.72 1.2319 1.4a57 1.6795 2.0203 2.3923
12 13.18 1.2479 1.5011 1.6939 2.0326
13 14.10
2.402 !
1.2599 1.5116 1.7032 2.0398 2.4073
13 14.56 1.2731 1.5239 1.7146
14
2.0491 2.4144
15.49 1.2831 1.5326 1.7221 2.0547 2.4183
34 15.W 1.2939 1.5425 1.7310 2.0617
15
2.4234
16.88 1.302S 1.5497 1.7371 2.0661 2.4263
15 17.34 1.3118 1.5581 1.7445 2.0718 2.4302
16 18.26 1.31s7 1.5638 1.7493 2.0751 2.4323
16 19.65 1.3484 1.5911 1.7739 2.0940 2,4453
16 20.60 1.3755 1.6184 1.7999 2.1161 2.4620
97
1------- -—. . .. —. —___ ____
MIL-HDBK-781
TABLE tO&. (I-Y ) 100peccent standard confidence Iim!l! on MTBF af!er reiect decmon
(upper - @j ( Y. 1 )) (Continued)—..
UPPER CONFIDENCE LIMITS FOR MTBF 6 ON THE REJECTION BOUNDARY
IuMEIER OFAlLURES
a3445
:677
88
TEST PLAN IV-O
=--k’.70
2.082.803.464.1 B4.865.506.246.967.628.3A9.74
.4171
.8127
.89141.02841.07341.16341.19101.247B1.26541.30311.31471.3763
I = 2.0,-
Y = .30
.63791.15491.24181.40841.45411.55511.58161.64131.26541.69481.70491.7664
7= 0.20
Y = .20 Y =.10
&1911.46061.5517I .73791.7B301.88911.91391.97331.9B762.02322.03182.0895
1.31632.09162.18632.39982.441B2.55062.57\62.62672.63772.66772.67372.7203
Y = .05
1.96982.91333.00783.24023.27743.3B193,39863.44553.45333.47s93.47973.5124
LIPPERCONFIOENCL LIMIT5FORMTBF80N (HFREJEmlON BOUNOAR”f
TEST PLAN V-D d = 3.0, a=~=o.lo
NUM8ER OF TOTALFAILURE5 TEST TIME Y = .50 Y = .30 Y = .20
(t)Y=.lo Y = .05
234455
.572.223.753.875.405.527.057.178.70
10.35
.axgb
.85141.09931.1275!.28161.30071.40301.41641.48661.6326
.51941.20131.49661.53221.70201.72451.B3041.84511.91422.0766
.69141.51041.83731.B7832.05572.08022.18552.20092.26662.4352
1.071B2.13872.51102.56092.74342.77032.86952.88502.94213.1097
1.60402.94053.34783.40573.5W83.61293.70103.71553.76143.9145
98
.
MIL-tiDllK-781
TABLE 10B. J1-7) 100 oercent standard confidence limits on MTBF after reiec( decision
(upper- c?~,(y,t)) (Continued)
UPPER CONFIDENCE LIMITS FOR MTBF#ON THE REJEC710N BOU8JOARY
TEST PLAN VI-D d = 3.0. a=@. o.20
NUMRER OFFAILURES
(t)
U?%!? CQNF!QENCE L!MITS FOF! MTBf 4 ON THE REJE~lQN BOUNDARY
TEST PLAN VII-D d = 1.S, a = ~ = 0.30
I I 1 I&~~&°F I T~~E 1 Y = .S0 I Y= .30
I 1Y = .20 Y -.10 Y=.05 I
3 I
I
1.2? I .4562 I .6375 I .79* 1.1070r 1.49204 2.43
!
.6856
I
.9211 1.1183 l.496I ).9450 15 3.15 .7s0! .9921 1.1927s I 3.65 I .8322 I .1.0898 1.3009
;91 ;~l
1-A.3-)
:~
Im: I i.i335 \ .3446
S.58I ,.>142 I ;:;;:
! .54305 6.80 1,7939
;:;::; ~ ::;;;; ~
I J
iJPPCR CONFIDENCE LI,vo, ,‘“’7$ FOR MTBF 8 ON THE REJECTION SWF!DAF!Y
TEST PLAN VIII-O d = 2.0. a= @ . 0.30
%utvmcn wr. .. ...” -. I I
FA.ILLIRES
I
?E%%E ~ Y= .50 Y = .30 -7 = .20(1)
Y =.10 Y = .05
I3 1.72 .6432 .5%7 1.1205~ 3.19
i .5607 2. IG351,1!2! 1.5594 1.9473 2.717) ~,~~s~
3 A,so 1 3867 1.9710 2.4763 34779 I 4.7114
MIL-HDBK-781
TABLE 11. Summarv of fiwd-duration lest olam
“-1 Plan
IX-DX-D
xl-D
XII-DXIII-DXIV-D
xv-cXVI-D
XVII-D i
True
deci$ionrisks
(percentage)
=-+12.010.919.7
9.69.B
19.9
9.410.917.5
9.921.419.610.6
20.921.0
9.921.319.7
+1.5 45.01.5 29.91.5 21.5
2.0 lB.8
2.0 12.4
2.0 7.8
3.0 9.3
3.0 5.4
3.0 4.3
TA8LE 12, Summa wofh, ahnsk fixed-duration test olam.
Number offailur~
=
.137 3626 25lB 1714 1310 9
6 56 54 33 2
True
decisionTest Plan risks Discrim, nation
(percentage) ratio (d)#O /@l
a B
IXIX-DXX-D
XXI-D
29.B28.330.7
30.1 1.528.5 2.033.3 3.0
Testduration
(multiplei
of e,)
8.13.71.1
Number of
failures
Reject Accept
(equal (equalor more) or Iew)
7
I
63 21 0
100
MIL-HDBK-781
TABLE 13. ~n.
I I CONFIDENCE INTERVALS 1
80 PERCENT II t 40 PERCENT I 60 PERCENT
II I
4490 90PERCENT PERCENT
LOWER UPPER
LIMIT LIMIT
0.434 9.491
ITOTAL NUMEER
OF FAILURES
I70:PERCENT:LOWER
LIMIT
70
I
80PERCENT PERCENTuPPER LOWER
80PERCENT
uPPER
LIMIT
%i%-! 1 ,0.801 4.481
I0.820
0.030
1.823 i 0.668 2.426
0.564 2.722
0.599 2.293
0.626 2.055
0.647 1.904
0.665 1.797
0.680 1.718
0.693 1.657
0.704 1.607
0.714 1.567
0.723 1.533
0.731 I .504
0.738 1,478
1.745 1.456
).75 1 ).437
).757 1.419
1.763 1.404
3.767 1.390
).772 1.371
2.806 1.291
E3
4
5
6
1.s68 10.70! 1.954
1.742O.mo 1.447 i 0.725
1.376 ,0.744 1.618
1.537
0.849
0.856 1.328 10.759
I 7 10.863 1.294 10.771 1.479
l-+--k= 1.4351.267 0.782
1.400
1.372
1.247 0.796
I 10 10.878 =-l=-1 11 0.882 1.215 0.B06 1.349
=
12
13
14
0.886 1.203 ,0.812 1.329
!.3120.889 1.193 ,0.818
0.892 0.823 1.2971.184
I I 15 10.895 1.176 i 0.828 1.284
E=E1.272
1.262
1.157 10.840 1.253
.!52 10.843 I .244
I 20 10.906 .147 0.846 1.237
I 30 0.920 .115 0.870 1.185
101
MIL-HDBK-781
TABLE 14. Demomtrated MTBF confidence limit multiplier%. for Ibme calculation.
I CONFIDENCE INTERVALS
! 40 PERCENT 80 PERCENT .
I tI I
II
I
I II&E~ ‘;iE~ I ~;: ‘:RCENT
l~RcEN~ ‘~RcEN~ ITOTAL NUMBER uPPER I[ LOWER uPPER
10F FAILURES 1 LIMIT LIMIT I LIMIT LIMIT I LIMIT I LIMIT II 1 10.41O 2.804 I 0.334 4.481 I 0.257 9.491
, , I
i 2 i 0.s33 i 1.823 i 0.467 i 2.416
I I
1; 6.6;0 1.568 ~C.s.$.$ ~ : .s54
I 4 10.679 ! 1.447 I 0.59s I ,.742
s 10.7,4 ‘ 1.376 10.632 i 1.6,8
6 0 7C9 !. 328 0.55! ~ 1.537
! 7 ! 0.760 1.294 10.6EM I 1.479
0.376 13761 i
. ..- I
-0.539 1205s I
i8 ‘0.777 ~1.267 ]0.703 11.43S ~0.6,6 ,7,B ~
I
~,??o9 , 1.2C? !2?!9 ! .4L?!2 ~.~~a
I
I
1.55?
10 10 B02 I 1.230 0.733 I 1.372 [0.649 1.607 I
11 0123 1.215 0.744 1.349 0.663 1 567.1
!2 0.s2 ! ! .Icf: 0.?55 1.329 0.675 :.533
13 10.828 1.193 0.764 1.312 0.686 1.S04
114 0.B3s 1.184 0772 1,297 ~ 0.696 1.478
f~ @.84! ?.!?5 o,?:~ 1.2%i
I 16 10.M7 I 1.169 10.787 I 1.272 10.713 1.437
17 0.8S2 1.163 0.793 1,262 0.720 1.419
18 ~.&~ !,!~? 0.7?9 ! ,253 0.727
I
! .404
19 10.861 1.1s2 10.804 1.244 0.734 1.390
20 0.864 1.147 0.809 1.237 1.377
~g 0.891 :.?15 0.844 ?.:85 ~0.7L33 1.291
102
MIL-HDBK-781
1.
I
Tesl Plan Accept times 11
IX-D 10 = 4.2 T, = 6.1 T2 = 7.9 T3 = 9.4 T4 = 11.0
I75=12.6 16 = 13.9 1, = !5.3 TB = f~,~~9 = :=. C
TIC = 19.3 TII = 20.7 T,z = 22.0 Tf3 = 23.3 T,. = 24. S
IT,5 = 25.8 T16 = 27.1 T,, = 28.3 TIB = 29.6 T19 = 30.8
1,20 = ,2,;
I
r~, = 3;.3 72* = 34. !i ’23 = SS.8 ~24 = 3~.o
T25 = 38.2 T25 = 39.4 127 = ao.6 T2e = 41.8 T?! = 43,0
Tao = 44.2 TX, = 45.4 T>2 = 46.6 T33 = 47.8 Tla = 49.0
T15 = 50.1 ?~~= 51,3 737 = 52.5. . . .
1~~ = >. J./ , 39 = 54.6
T:. = 56.0 7:! . 57,2 T42 = 5$,3 1:3 = 59.5 TC4 = 60.7
Ta5 = 61.8 T46 = 63.0 T4, = 64.1 TaB = 65.3 Tag = 66.5
150 s 67.6 T5, = 68.8 T52 = 69.9 T53=71. i T5a = 72.2
x-D 10 s 3.2 11 = 5.0 T2 = 6.6 T? = 8,1 T. = 9.5
T5 = 10.9 T6 = 12.2 T, = 13.6 Ta = 14.9 T9 = 16.1
ijo = 17.’s T,, = 1S.7 T,~ = 13.5 .!,j = 2;.2 7,4 = 22..i
T15 = 23.6 T16 = 14.8 1:7 = 26.1 TIE = 27.3 T,g = 28.4
I ,.. -. ,-,, . ..=..“e, -”,,,-” “. ,,,= “,”. ”,,,,”~..-..
MIL-HDBK-781
“TABLE 15 ~eat time> 01 f,aed-duration test plans. Proaram Maria Qer’s assessment (Continued)
‘km flan
x-DCnnt’d)
Xl-D
XII-D
XIII-D
Accept tim~ 1;
T>. = 29.6 121 = 30.8 T22 = 32.0 T23 = 33.2 TIO = 34.4
T25 = 35.6 T26 = 36.7 127 = 37.9 T28 = 39.1 T29 = 40.2
130 = 41.4 T31 = 42.5 T,z = 43.7 113 = 44.8 T34 = 46.0
T3j = 47.1 T36 = 48.3 T,, = 49.4 T38 = 50.6 139 = 51.7
10 = 3,0 T1 = 4.8 12 = 6.3 13 = 7.8 To = 9.2
15 = 10.S T6= 11.9 T, = 13.2 18 = 14.4 T9 = 15.7
TIO = 17.0 Tll = 18.2 T}2 = 19.5 113 = 20.7 T1a =21.9
T15 = 23. ! T,b = 24.7 117 . 25.5 T18 = 26.7 T19 = 27.9
T2U - 29.1 T21 = 30.3 T22 = 31.4 T2, = 32.6
To = 3.7 T, = 5.6 T, = 7.2 T3 = 8.8 Ta = 10.3
T5 =11,7 T6= 13.1 17= 14.4 Ta = 15.8 T9 = 17.1
110 = 18.4 Tll = 19.7 T12 = 21.0 T13 = 22.3 T,a = 23.S
T,, = 24.8 T16 = 26.0
To = 2.8 T1 = 4.6 T2 = 6.1 T3 = 7.5 la = 8.9
1$ = 10.3 T6 = 11.6 T, = 12.9 T8 = 14.1 T9 = 15.4
T,. = 16.6 T,, = 17.9 1,~ = 19.1
I/Accept at time (Tj) if (j) failures have occurred up to that time
104
MIL-liDBK-781
TABLE 15. ACCeDt limes of f iaed-duration test olans. %aram Manaaer’s assessment. [Continued)
Test Plan I Accept times 1/
XlV-D To = 2.7 1, = 4.4 T2 = s.9 T, a 7.3 T. = 8.7
T5 = 10.0 1~ = 11.3 T, = 12.6
XV-D TO = 3.5 T, = s.4 T2 = 7.0 T, z 8.6 T. = 10.0
T5 = 11.4 T6 = 12.8
XVI-D TO = 2.5 T, = 4.1 T> = s.6 la = 7.0 T. = 8.3
XVII-D TO = 2.2 T, = 3.8 T2 = 5.2
X( X-D T* = 2.1 T: = 3.7 T2 = S.1 Tg = 6.4 76 = 7.7
T5 = 8.9 T6 = 10.2 77 = 11.4 TB = 12.6
XX-D TO = 1.8 T, = 3.2 T2 = 4.5
XX I-D To= 1.1
l(ACCepi at time (T;) if (j) failures have occurred up to that time
I
1’I
105
I
MIL-HDBK-781
TABLE 16. Compa<iwn of risks, sfandarci fixed-duration tests versus Proqram.Manaaer’s asses~me?!
Standard test plans Program Manager’i assessment
Ten Discrimination Producer’s COnwmer’s Producer’s Corwumer”sPlan ratio rmk a(%) risk ~(%) risk a(%) risk ~(%)
IX-D 1.5 !2.0 9.9 10.2 10.0
x-D 1.s 10.9 21.6 10.1 29.8
Xl-D 1.5 17.8 22.1 20. I 20.4
XII-D 2.0 9.6 10.6 10.4 10,3
XIII-D 2.0 9.0 20.9 9.9 19. >
XlV-D 2.0 19.9 21.0 20.0 18.3
XV. D 3.0 9.a 9.9 10.0 8.d
XVI-D 3.0 10.9 21.3 10.2 18.7
XVII-D 3.0 17.5 19.7 19.7 19.2
----- - ----- -- ----- ----- ---- ----- ----- ---
(High ri$k pia ns)
XIX-D 1.s 28.8 31.3 29.6 30.8
XX.D 2.0 28.8 28.5 29.9 29.1
XX I-D 3.0 30.7 33.3 30.7 33.3
106
I
S:ahalu e,. J-.t..J. a .,......, Program Manager’s zssessmenl
#I 1
Te\tI
I “’c’: y;,y”o” I ,::, ~“m$;;;;;i”’e’ I ,~:,, ‘“o’&:;::’”’”?Ian
I;X-D i
I
;.5
I
l?5,cl ~37 i
I
72.2 ~ 55
x-D 1.5 29.9 ~ 26 51.7 ~ 40
I I ,,,6XI.D 1.5 2!.1 ~ 18 ~ 2ii
X!!-D I2.0I
!9.9 > 1A Zfi.(l ~17—
XIII. D I 2.0 I 12., ~ 10 19.1 ~13
XIV-D I 2.0 7.U 26 i2.6 ?~
XIV D
I3.!2OJ26 12.8 27
XV1.D 3.0
1
5.4 24
I
8.3 ~s
XVII-DI
3.0 4.3 ~ 3
t
5.2 23
.. ----&- ------- -------- ---- —-- --------(High r,$k P!am!
XIX-D I 1,5 8.0 >7
1
12.6 29
XX.D 2.0 3.7 ~? 4.5 23
~~,.~ ~.fi !.1 >1 1.1 ~1—I
!/Multiples of 6’:
107
MII.-HDBK-781
..— .—. _.. — .—. —
. .
m
108
)
.-
18 ,, 0, ,, u
-- r.- c- .- c
=, 2, .% a, >,
.
.
.
.
.
.
.
TABLE 19 Example of correct order, na in the AO bound calculation
fort o relibd2
runGtve number of $ubsystem$.3Enler data starting by subsystem wi!h smallest total time on test.~=~er ~~~~ f~r j“b$ystem 1
Enter Ih,$ wbsystern”s total time on test14.61
Enter this wbsystem”s number of failures2
Enter ciaia for $ub$y%leirl 2Enter th, s subsystem’s iotal time on te~t35.971Enter th, s subsystem’% number of failure$.2Enter data for subsys:em 3Ente, th,swbsystem’s total time on test
62.542Enter th,s subsystem’s number of fa,lures
2
Enter confidence level percenule1.282
Enter miwontome1.0
Mission Time: 1.00000Percentile: 1.2B200
M2 = 0.1806820 V2 = 0.0103983R.41abi:iiy B&tinci is: C.72L?5C19
If another confidence level or miwon ume, gtve 1.1
Enter confidence level percentile0.0Enter mission time1.0
Mission Time: 1.00000Percentile: O.
M2 = 0.1806820 V2 = 0.0103983Reliab,l,!y Uound ,$ 0. ft50297
If another confidence level or m!won time, gove 1
0.
109
M:L-14E213K.781
!
.
.
.
.
.
.
.
.
.
run
G!ve number of subsystems3
Enmr ciala slan, ng by sub}ystem with \flldlle$t iOial hme on test
Enter data %: ;u!xjj$:efl IEnter th;$ wbsys?em’$ total time on test
35.971Enter this wbsystem”$ number of failures
14.61
Enter this subsyslem’5 number of Ia,lures2Enter data for subsystem 3
Enier Lhis subsystem’s total tome c.r, te$t
Enter confidence ievei percenuie; .~:~
Enter rn!ss!on urn?1,0
Miwon T,me. 1.00000Percenuie: i.ia200
V.2 - 0.14003s9 V2 . 0.0064862Reliability Bound ,s: 0.780768
If anolher confidence level or m,sslon ttme. g,ve 1
1
Enter mwsmn time.1.0
M!s!oc ?!me; 1.90000Percentile: O.
M2 = 0.1400359 V2 = 0.0064662
Rellab, i!ty Sound i5: u.Ex+.23M
If mother confidence level 0: ,m155im tf,me, give 1.
0.
110
MI L-HDBK-781
Eza~, ple ru,n: I Reference 13, page 200. !ine !
I,th Subsystem Totai i,me on teslI
Number Fa, !ures
1 9.919 4
I2I
15.995 ~
3 I 26.897 I 2
IA
I26.511
I3
~~,~:g I5 3
.
.
.-.
.
.
.
MIL-HDBK-781
TABLE 22 Examglecomputer run for data #n TAEILE 21
7117,
Give numh?r of s,.,bsystems5
Enter data starting by subsystem w!th smallest total tame on lest,Enter data for subsystem 1
Enter this subsystem’x iotal :Ime on iesl9.9!CEnler this subsy~tem,s number of fai!ures
4
Enter data for subsystem 2Enter thi! subsystem “s total time on test; 5.2%%ler l!.Is .ss~.-=*-F,’5 .rw-bw C! fa:luws.’. . . . . . . . .2
Enter data for subjystem 3Enter th, s subsystem’s total tfime on lest26.G97Enter th!~ wbsysteP,,s n,~mbpr of f*,l,ures
2Enter data for subsystem 4Enter this wbsystem’5 total ttme on test25.511
En:?r :tvs sutxy;:ern’s ntimber c! !ai!u:e;3
Enter confidence level perce”t,le1.282
Enter miwon !time1.0
Mission Time: 1.00000
Percentile. 1.28200
Ml = 0.5946215v1 = 0,0475423
.%!%lli:y BGund is: 0.412537
M2 = 0.5058325 V2 = 0.0491630Reliability Bound is: O.4O61O1
M3 = 0.5899235 V3 = 0.04ti57b4
Reiiab, i,iy Sound 1$: 0.415676
If another confidence level or m!ss, onl, me, ?,ve 1.
0
112
I
MIL-HDBK-7B1
TABLE 23 Thermal stress environments for marine craft
Envmonmental Opera(ing Nonoperalmg
condltjon “c “c
Exposed-unsheltered -S410 +65 -6210 +71
Exposed-unsheltered -2810 +65 -6210 ●71
(thtp)
Sheltered noncontrolled 40 to ● 50 -6210 .71
environment (!hore)
Sheltered noncontrolled 010 +s0 -6Zio ●71
113
TA
BLE
14.
Env
ironm
enta
lor
ofile
data
(exa
mD
lej
D
CO
MP
AR
T.
oY-
ME
NT
TE
MP
ER
A-
NA
MIC
DE
WP
OIN
T7E
MP
ER
-lU
RE
FM
7EP
RE
S-
TE
MP
ER
A-
DU
RA
TIO
NA
LTIT
UD
EA
TU
RE
OF
CH
AN
GE
SU
RE
w.
w,
TU
RE
MIS
SIO
NP
HA
SE
(MIN
UT
ES
)(1
000
FT
)M
AC
H(~
c)[o
CP
ER
MIN
)(q
)(a
1/H
z)(a
2/H
2)(O
c)
GR
OU
ND
NO
NO
PE
RA
TIN
G,
300
-54
CO
LDO
AY
NIA
GR
OU
ND
OP
EIU
TIN
G,
30C
OLD
OA
Yo
-54
N/A
TA
KE
OF
F1
00,
601.
830,
002
0.00
1N
IA
CLI
MB
TO
ALT
ITU
DE
111-
340.
6028
00.
0005
0.00
025
N/A
CR
UIS
E18
340.
55-3
211
00.
0000
80.
0000
4N
IA
DIv
E4,
2534
-o0.
853.
0554
10.
0019
0.00
09N
IA
CR
UIS
E45
00.
60-1
954
10.
0019
0.00
09N
/A
CR
UIS
E(C
OM
BA
T)
50
0.83
-10
1024
0.00
70.
0035
NtA
CR
UIS
E45
00.
60-!
954
10.
0019
0.00
09N
IA
CLI
MB
70-
350.
701.
8537
50.
0009
0.00
045
NIA
CR
UIS
E18
350.
45-3
276
0,00
004
0.00
002
NIA
OE
SC
EN
OT
OH
OT
DA
Y14
35-o
0.40
7.35
!24
0.00
0I
0.00
005
NIA
GR
OU
ND
NO
NO
PE
RA
TIN
G,
300
.71
31
HO
TD
AY
GR
OU
ND
OP
ER
AT
ING
,30
0+7
13!
HO
TD
AY
TA
KE
OF
F1
00,
605.
000,
002
0.00
1N
/A
CLI
ME
TO
ALT
ITU
DE
111-
340.
6028
00.
0005
0.00
025
N/A
CR
UIS
E18
3d0.
s5+1
111
00.
0000
80.
0000
4N
/A
DIV
E4,
1534
-00.
8514
.154
10.
0019
0.00
09N
/A
CR
UIS
EA
So
0.60
+71
541
0.00
190,
0009
NIA
CR
UIS
E(C
OM
BA
TI
so
0.83
+71
1024
0.00
70.
0035
N/A
ER
UIS
E4s
o0.
60+7
154
10.
0019
0.00
09N
!A
CLI
MB
70-
350.
708.
7137
50.
0009
0.00
045
NIA
CR
UIS
E18
350.
45+
1076
0.00
004
0.00
002
N/A
2E5c
EN
DT
OC
OLO
OA
Y14
35-o
0.40
4.57
124
0.00
010.
0000
5N
IA
I
IIGROUNO NONOPERATING,
COLD DAY
IGROUND OPERATING,
CGLi3 i)AiTAKEOFF
I CLIMB To ALTITUDE
I
CRUISEDIVE
i
CRUISE
CRUISE (Cc3Liii Ai)
I :~~0:
I DESCEND TO HOT OAY
IGROUND NONOPERATING,
HUT DAYGROUND C? ERATi:dG,
I TA%~~vI CLIMB TO ALTITuOE
I CRUISEDIVECRUij E
CRU15E (COMBAT)CRUISECLIME?
I CRUISEDESCEND TO COLD DAY
TABLE 25
3URATION
;MINUTES)
30
30
?..4
182.6
45
5q~
26181A
30
30
1
11
184.2S
45
5As
7
18
13
MIL-HD8K-781
Test profile data (examrie~.
~~$wq~A~~.
WENTTEMPER-
ATURE
rc)
- Sd
-54
-32
-19
- ii)
-19
-32
+71
.T1
+11
.71*7!
+71
+ 10
5.0
5.0
S,(I
7.35
5.0
14.1
8.71
S.o
1-1-
(),~~~
0.001
10.00110.0019
I :::;9
I
,-,l-,n, a. .. . . .
,:::;
1-
0.001
1-
10.002
1
0.001
0.001
0.0019
, p0;9
10:0019
I0.0010,001
0.001
op.AJ.
POINT
tEMPER-
ATURE
rc)
N/A
N/A
NIAN/AN ,4N;A
N1AI.I:A
PL’AN/ANIA
N[A31
31
N:A
N;A
N/A
NIA;4,,~
F!!AN/A
N/AN/A
N/A
QIJIP.
nEt’JT)PERA.
‘ION
oFF
ON
OF!
ON(2NON
ON
GN
0!!ON
ON
ONOFF
0?:
ON
ON
ON
ONON
ONONC)N
ONC)N
I
i15
MIL-HDBK-781
; ti,i, ! .?6 , ,,,&t-ernPeratur eflQor Class. &~>ment in a,~-condl~ooned compartments.— -
ALTITUDE TEMPERATURE
( 1000 FT) (“c)
o 5510 5320 40
30 4040 3050 20
TABLE ?1 ;Hot dav arnb, ent temperature (“C) for Cla$s II equipment #n a,r.conditioned comoarrmems
\ HIGH
LTITUDE PERFORMANCE
000 FT) ~ 0.6 0.8 1.0 ~(1.o)~’
o 71 71 71 95
10 S6 68 68 93
20 40 55 63 88
30 15 36 56 80
40 5 10 46 70
50 5 10 35 60
60 5 10 24 49
70 5 10 11 35
l’Ambaent cooled equtpment must be turned off for 15 m!nules after 30min U1eS0f OPerall On
at these Iemperalures to comply with the Interm)tten! operat, on of MIL. E.5400
116
i
MIL-HDBK-781
TABLE28 Holdavambient tem?eralures ~C)!oreauiPment inramair-coGled c0mPar1ment$
o
10
20
30
40
50
60
~o.d
40
27
6
-15
-36
-30
-31
-30
0.6
60
38
16
-6
-30
-19
-23
0.8
75
52
29
7
-16
-7
-11
70 -22 -10
~,Amb, ent cOOled CIa~S Itequ,pmentmust be turned off for 15m, nule$ after 3
~(1.o)
95:’
71
A6
23
-1
0
A
5
!nute~ of.,operation at Ihi! temperature to comply w,rh tne ,nterml ttentoperal, on requt~ement of
MIL-E-5400.
TABLE 29 COlddav amb, enltemperatures ("C) foreQuipment inrama, r-cOoled comparlmenIs
o
10
20
30
40
50
60
~oxt 0.6 0.8 ~(1.o]
-44 -37 -15 -11
-18 -10 2 t9
-36 -28 -16 -2
-58 -50 -40 -27
-59 -51 -41 - 1s
- B2 -76 -67 -55
- B2 -75 -66 - 5L
-65 -58 -48 -35
117
MIL-HDBK-781
TAtI1 F 30. ~Inpy,.?mres (“C) for Clas~ I and cla~! Il?auic. men: in air-conditioned cOmc@flmen:S
‘wARM COMPARTMENT
r’
‘1 0 : ;MACH HIGHAI. I’ITu DE NUMBER to PERFORMANCE
yE:::.59 .79 ~ 1.0
8 12 19 27
1 ‘o ,,) i 24 2Y 36 4A
i u 16 20 27 35
30 7 11 17 24
40 8 12 17 24
W 6 9 14 21
COOL COMPARTMENT
ALTITuDE(1000
PERFORMANCE
FEET)
o -26 -19 -10 2
21010 -4 3 13 27
20 -17 -10 -1 11
30 -32 -26 -17 -6
40 -33 -27 -18 -8
50 -38 -32 -24 -14
118
MIL-HDBK-781
TABLE 31 Jet aircrafl random vibration :es:
Aerodynem, c induced vibratmnWO . K(q)~, where q .WI = WO-3dB
Dynam)c pressure (when q> 1200 Ibs/ft 2, use 1200)
(SEE FIGuRE 65 for spectrum $hape)
K Localmn Factor Equ,pment Iotalion
0.67 X 10.$ Equipment attached to structure adjacent to external surfaces that aresmooth, free from dosconttinuiloes.
0.34 x 10-8 Cockpll equipment and equipment in com artmentf and O? shelves adjacentrto external surfaces that are smooth, free rom da$contlnumes.
03.5 x 108 Equipment attached to structure adjacent to or immediately ah of $urface\having dtscont,nu)tles (that is, cawtie!, chins. blade antennas. and so fOnh)
01.75X lo.e Equ,pment ,n compartments adjacem to or immediately aft of surfaces hawngdisconl!nu,lles (that,$ cav,tles. chins. soeed brakes and so for!h)
SPECIAL CASE CONDITIONS
FIgh!er bomber
Cond,l,on Equipm?nt Iocauon WV
Takeoff A(tached to or #n compartments adjacent to structure direclly exposed to 0.7eng, ne exhaust ah of engane exhau$iplane(l minute)
Cruise (Same as above) o. t 75
Takeoff In eng, ne companment or adjacent to engine forward of eng#ne exhaustplane (1 m,nute) 0.1
Cruise (Same a$ above] 0.025
Takeoff. Iand,”g, Wing and fin tips L/ deceleration (fpeed brake) (1 m,nute) 0.1maneuvers
High q W,ng and fun tam V(> 1000 lbs/ft2)
0.02
Cruise Wing and fun COpS3 0.01
Takeofl All other Iocat, ons ( 1 minute) 0.002
Cargoltranspon
Cond,t,on Eau, Pment Iocat, on w ~
Takeoff Fuselage mounted O.c I
Takeoff Internal 0.005
Takeoff Wtng -ail of eng, ne eanaust Q 0.05
All Wtng I,LI and f#nt#p2 O.c I
1 Use wing and fln IIP specuum (see F!GURE 65)
J Excludes LIpOer wrface blown (USB) and e~ternallybiown flaP(E:a~
>/ 7ak.eoff, land, ng, plus 10percenl of cru, se time
119
. .
TA
BLE
32T
abul
atio
nof
Iem
uwal
we
Val
ue$.
❑C
OLD
DA
Y
❑H
OT
DA
V
TE
MP
ER
AT
UR
EO
UR
AT
ION
wE
IGH
TE
DD
UR
AT
ION
I
MIS
SIO
NB
WE
IGH
TIN
GF
AC
IOR
=M
ISS
ION
AW
EIG
HT
ING
FA
CT
OR
- WE
IGH
TE
DD
UR
AT
ION
WC
IGH
TE
OD
uRA
TIO
N
Sum
mar
vof
tem
pera
ture
valu
es.
❑C
OLO
DA
Y
TA
BLE
33
mH
OT
OA
V
,I
—
TE
MP
ER
AT
UR
EV
ALU
ET
OT
AL
WE
IGH
TE
DD
UR
AT
ION
MIL.HDBK-781
TABLE 37. Temc.erature level tabulation - ho! dav (example~
kliigh.low-low-ht9h
Weighfing factor = 0.40
Low-low-highWeighting factor = 0.25
Close wppoflWeighting factor = 0.20
IFerryWe, ghting factor = 0.05
Temperature Level
(“c)1)
71
367110
71
23
366410
23
I
MIN = 10”Cfor43 minutesMAX . ?I”C {of M minutes
INT = 35.8°C for 77 minutes
,NT . 23(27) . 36(38) ● 64(12j . ~ = 35827.38+12 7? ‘
1.
Duration
(Minutes)
145
601770
7s
60
70
607s
240
Weighted
duration
14.s
24.010.8
28.0
!8.7s
1s.0
14.012.0
15.0
;2.0
TABLE 36. Temperature summarv - hot dav (examole~.
Temperature Level Total Weighted Duration
[“cl (Minutes)
10 43.0
23 27.036 38.064 12.071 44.0s
123
fw5iL-i+WiC-7~i
~
Temperature Level Durauon~ (Minutes)
Weighted
(“c) !! duration
.Ow.low.low
Weiqhltnq factor = C!.1O I
I
-26 145 14.5
High-low.10w-high I I IWeighting factor = 0.40 -26
1
130I
52.0
I
_iG 27
I
!C.s
Low-low-high
1
IWeighung factor = 0.25 -26 140 I 35.0
Close wpportWcI@wIng fa:tcr = !2.?0 1 -26
I
70 I 14.0-4 60 12.0
-27
1
75 I15.0
FerryI
I
We., ghr, ng f;ctw = 0.35!
?5f
~4~
!
IZ.Q
~, 5ele~ted Ievel$ and du,alionf (see 5.6.2.2)
MAx = f - 10) [10.8) + (-4) ( 121 = - 6.8°C for 22.8 minutes10.6 . 12
-27 {It .FAIN = L !- 25) [!2?.5J = - .26. I’C ior 142.5 minutes
15 - 127.5
$ince no level$ remain to select INT value
MIN = -26. l-C for 71.25 minutes andINT = - 26.1 °C for 71.25 minutes
TABLE 40. Temperature wmmarv - coia dav (examDie]
I TemperMure Level
I
Total Weighted
rc) Duration (Minute3)
-. 1S.o
-26 I 127.5-10 I 10.8 !4
I!
12.0!
124
I....._._._._...
TA
BLE
34
MIS
SIO
NA
WE
IGH
TIN
GF
AC
TO
Rs
—JI
BR
AIIO
NLE
VE
L(g
~i
n,)
——
002
001
---1
--D
UR
AT
ION
WE
IGH
TE
D
(MIN
)O
UR
AT
ION
1
...
..
..
..
..
Tab
ulat
ion
ofvi
brat
ion
Ie.e
ts
❑C
OLD
DA
Y
OH
OT
DA
Y
,
MM
ION
8W
EIG
HT
ING
FA
CT
OR
-h
.M
ISS
ION
XW
EIG
liTIN
GF
AC
TO
R■
7VIB
RA
TIO
NLE
VE
LD
UR
AT
ION
(gl/H
z)
002
101
—i–
..
.--
---
-.-.
..
..
..
..
..
-+-
WE
IGF
+T
EO
OU
RA
TIO
N
----
----
--,
TA
ELE
35S
umm
ary
ofvi
brat
ionl
evel
$
❑C
OLD
OA
Y
❑H
OT
OA
Y
r1
II
VIE
07A
TIO
NLE
VE
LlT
oTA
LwE
IGH
TE
OO
UR
AT
ION
I
002
100
1.
..
..
..
..
..
..---
----
---
----
----
----
----
----
----
----
TA
BLE
36.
-site
test
mof
i!eti~
~e.
N N
1
TE
MP
ER
AT
UR
E
EM
PE
RA
TU
RE
TE
MP
ER
AT
uRE
DU
RA
TIO
N17
AT
EO
FC
HA
NG
ED
UR
AT
ION
\TA
IITV
IBR
AT
ION
VIB
RA
TIO
N
PH
AS
EV
ALU
E~
C)
DU
RA
TIO
NS
TA
R
(MIN
UT
ES
)(“
C/M
INU
TE
)(M
INU
TE
S)
TIM
EP
HA
SE
VA
LUE
(gW
-!z)
(MIN
UT
ES
)T
IME
NO
N.O
PS
OA
KN
OV
IB
OP
SO
AK
TR
AN
SIT
ION
TO
II
INT
j!
TR
AN
SIT
ION
INT
MA
XM
AX
TR
AN
sIT
ION
MIN
MIN
11
TR
AN
SIT
ION
~!
NO
N.O
PS
OA
KN
OvI
E
OP
SO
AK
TR
AN
SIT
ION
(()
y
INT
j!
TR
AN
SIT
ION
INT
MA
XM
AX
TR
AN
SIT
ION
MIN
MIN
~.
TR
AN
SIT
ION
?
NO
N.O
PS
OA
KN
OV
IE
~T
AI(
Eo~
F
~,
O,O
OIg
?/Iiz
AS
RE
QU
IRE
DT
OA
SS
UR
EC
ON
Tl
NU
OU
SV
18W
T10
ND
UR
lNG
FLl
GH
TpH
A$E
$
,,,,,.
,,—,
--,
—,-
.,-,
.....-
,,,.
,-=
,,,,
_
c1 w
LOW
.LO
W-L
OW
Wei
ghtin
gF
acto
r=
.10
-H-
Vib
.D
urat
ion
Wtd
Leve
l(r
ein)
Dur
(g~
/Hz)
002
10.
1
l-ltake
olfi
001
140.
314
.03
0032
5.2
0.52
TA
BLE
42.
Vib
ratio
n
Vib
ratio
nLe
vel
(g//Hz)
.002
.00
I
.001
2
.001
5
.002
.002
6
.G03
2.0
041
.007
7
TA
EIL
E41
.V
ibra
tion
leve
lta
bula
tion
(exa
mpl
e~
tiigh
.Lo
w-L
ow.
H,g
h
ILow
.Lo
w.
H,g
hC
lose
supp
ort
Fer
ryW
eigh
ting
Fac
tor
..4
0W
etgh
liog
Fac
tor
..2
5W
e,gh
l,ng
Fac
tor
=.2
0W
eigh
ting
Fac
tor
=.0
5I
Vlb
Dur
,lliO
nW
ldV
!bD
urat
ion
Wtd
V,b
.D
urat
ion
Wtd
.V
ib.
Dur
atio
nW
td.
Leve
l{m
tn)
Dur
.Le
vel
(rei
n)D
ur.
Leve
l(r
ein)
Dur
.Le
vel
(rei
n)D
ur.
(g’/H
z)(g
>IH
z)(g
.’/H
z.)
(gW
iz)
.002
10.
4.0
021
0.25
.002
10.
2.0
02I
0.5
(Iak
eoff)
[Iake
ofi)
(Iok
eoff)
(tak
eolI)
.001
143
57.2
.001
142
35.5
.001
218
43,6
.001
259
12.9
5
.004
120
.78.
28.0
032
5.2
1,3
.001
26.
01.
2
.007
715
.06.
0.0
026
5.0
1,25
.002
2.5
0.5
.001
26
2.4
.001
55.
01.
0
!1su
mm
ary
(e~
am
Tot
alW
eigh
ted
Dur
atio
n(r
ein)
1,0
163.
28
3.6
1.0
0.5
1.25
1,82
8.28
6.0
?)N
OT
ES
:S
elec
ted
Leve
lsan
dD
urat
ions
:
1/0
=,0
02g2
/Hz
for
1m
inul
e
MA
X.
.007
7g~
/Hz
for
6m
inut
m
MIN
=.0
012
g~/H
zfo
r3.
6min
ules
lf4T
=.0
035
g2}H
zfo
r12
.85
min
ule~
(l)
.001
g21H
zfo
r16
3.28
min
utes
toas
sure
cont
inuo
usvi
brat
ion
(I)I
NT
=(.
0015
)(1
.0)
+(.
002)
(0.5
)+
(.00
26)(
1.25
)+
(.00
32)(
1.82
)+
(.00
41)(
8.28
)
1.0*
0.5+
125+
1.13
7+82
8
.045
522
.—
=.0
035
12.8
5
4 m
N m
FR
OM
LEV
EL
-54
°C
INT
c
MA
XC
MIN
c
+71
°C
INT
H
MA
XM
MIN
H
TA
BLE
43.
~er
atur
era
leof
chan
qe(e
xam
ple]
TE
MP
ER
AT
UR
ER
AT
fO
UR
AT
ION
TO
LEV
EL
OF
CH
AN
GE
C’C
)(M
INU
TE
S)
INT
C5
[(-2
6,1
)-(-
54)]
/5=
5,6
MA
X<
MIN
C
+71
°C
INT
H
MA
XH
MIN
H
-54
°C
7 5 8 6
!1.s
!0.5 6
[(-6
.8)
-(-2
6.1)
1/7=
2.8
jI-26
.1)
-(-6
.8)]
/5=
3.9
((71
)-(
-26,
1))
/8=
,2’.,
[(35
.8)
-(7
1)]
/6=
5.9
[(71
)-
(35.
8)]
/11.
5=
3.l
[(10
]-
(71)
]/1
0,S
=5,
8
[(-5
4]-
(10)
]/6
=10
.7
MIL.HDBK-781
I
I
127
MIL-HDBK-781
TABLE AS Random wbrabon test for V/STOL aircraft
Aero5pace Induced vibratton
WO = K(q)?, where q = dynamic pressure (whenq> 1200 ibdft2use 1200)W! = Wo-3dB
(K) Location factor Equtpment localion.—
0.67 X 10s Equtpment attached to slructure ad;acent to external wrfacej that are
smooth, free from discontirwi toes
0.34 x 108 Cockpit equipment and equipment in compartments and on \helves adjacentto external surfaces that are smooth, free from d,scont, nu, t#es
3.5 x 1O-B Equ, pine-m attached to structure adjacent to or ,mmecl, atelyahof surfacet
hawng d!$conl!nutl,es (tha[ !s, cavities, chins, blade an(enna$. and so forth)
1,75 x 10.S Equlpmenl en compartments ad!acent to or immediately aft of surfaces hav, ng
I dlsconttnult,es (that ,s, cawt,es. chfins, speed brake$, and so forth)—.
SPECIAL CASE CONDITIONS———
Cond!tton Equ!pment Iocatton WO(HORI ? WOWERT) 5
I I “K,.,. ,
TYF
A
Takeoff V Attached to or an compamments adjacent 0.7 0.0510 structure d,rectly ezposed to engtne
exhau$! ah of engine exhausl plane(1 minute) U
Takeoff Y In eng,m compartment or adjacent to 0.1 0.!7eng, ne forward O,l of engine exhausiplane ( 1 minute) U
Takeoff Y All other Iocat, ons(l minute) U 0.002 0.02
Y Takeoff or landing
ILl 0.5 m#nulesfor vermcal takeoff handing mode
.
128
)L
s
B
0.60
D.OA
0.02
I
. .
aJ
—QEmx
188
129
?.?! L- HDF!K.7s?
FABLt. 47 stores host a,rcraf! m,,sion ul!iizal, on. rates ior ewronmenlai testinq——.—.
Examole util, zatton_rates of mi\\ion profiles
I Mkon :, Percent Utilization RateI
1
I Ground Attack, Traamng
I
40
Ground Attack, Combat 20I
IGeienwve tianeuver% 2i2
I
sea::~, ~r,~ p.=>: .tic I
I!!? I
I
FuncT,mwl Check
~
5 ITra, ning Cycle 5 I
, ~~ J
lzSI”Ce It, e f!rstth,ee m~fsio”s, as a g,,., ,c., total 80 percent of the ultlizal, on ram, Ihe$e three mi%s,a-
profiles would be selected for comb, ned enwronmental tesung. II any oi the other mtss, om are
cielermfned 10 include extreme or Wstalned enwronmental CWidnifon$ IW1 eficourtiered ,r, [he f,,, !I , t, thereby x!dinqthe zc%tc?:ver:,:j.:c me:bl:ee 7,1; Y)071S,:h,er, ;!wse mIwcn\ a!; o :ho,a!d be m e:. e
!e$! cycle Illhe fir$! rntission <elected ,s utillzed twice mrnuch a\ the other two mns,ions, then Mnss, c,n
I should be run twuce as much per cycle. (See MI L.ST D-81O, Table 520.0-1)
130
I ,“, !”.... . . . . . .
MIL-HDBK-7B1
TABLE 48 Random wibratton. g,~ , (OVL). level ad;usfment factOr$ fOr the maximum predicted en.ironmenl(95th Percenllle wtth 50 percent confidence based on one-side tolerance Itm!t).
AIR. LAUNCHED g,,n, (OVL) MINIMUM
MISSILES AND FACTOR FOR DYNAMIC
ASSEMBLED BASELINE PRESSURE (Q)
EOUATION EXTERNAL STORES MAXIMUM BELOW WHICH FIGURE
CONDITION PREDICTED g,m, (OVL) = 1.3 NuMBER
(NU&ER) OF CONFIGURATION ENVIRONMENT (CONSTANT) APPLICABLE~1~f ~, y
COMBINEO1. MuLTIPLE-USE ALL 1.00 250 132
STORE (BASELINE)
2 SINGLE STORE o.aEl 264
3 CLUSTER MOUNT !.28 19s
AIR. TO. SURFACE (AGM)
4 Mu LTIPLE. USE 0.96 260 133
ALL STORES
5 SINGLE STORE 0.83 302
6 CLUSTER MOUNT 1.25 201
AI R.TO. AIR (AAM)
7 MuLTIPLE-USE I .07 235 I 34
ALL 5TORES
8 SINGLE STORE 0.97 259
9 CLUSTER MOUNT 1.38 182
1-
! THE MAXIMUM PRE21CTED ENVl RON ME NT(ASDETERMINED FROM mNDOMVlBWTlON
STAT15TICAL ANALYSES) IS OEFINEDEY +6dBLOG-LOG g,~, (OVL) VERSUS q LEVEL EQUALTO OR GREATER THAN THE 95TH PERCENTILE VALUE AT LEAST 50 PERCENT OF THE TIME.
SEE FIGURE 132 FOR THE BASELINE gr,n, VERSUS qFORALLsTORES
?’ CLUSTER MOUNT VALUES ARE ONLY VALIDFORaPTIVE. FLlGHTCONDlTlONS
Y EOUAT1ON OF LINE, g,m, VERSUS q(6dB10CTAVE ON LOG-LOG):(FROMi= 1T09) [gr~, (OVL)]l = (l OIEXP))T( BASELINEI
[exp]= [10g10(q)-(2.28 S33)l
[g,m, (OVL)li= (FA~OR)i [9rm~(OVL)], (B4sELlNE]
131
,. . . . . .. . . .. .. . ...-4 .“, , “,, ..,,,.”,..,.,,,. ma, m,,. ”r,.”,. m ,,, A,,,,”,. , .,”=,,”,,,, ,,nu= -”,, ,.””, . . .
TA
9LE
49M
e!ho
dof
~alc
ulat
ina
the
acce
lera
tion
gow
er$p
ectr
alde
n$itv
spec
trum
10pr
oduc
e
RE
FE
RE
NC
E
FIG
UR
EN
UM
BE
R
135
(a)
. N13
5(b)
f!‘eq
ual
10a
unit
-9,
m,(
OV
L)—
!.1
EO
UA
TIO
N
(ALL
PS
DS
LOP
ES
.M,
AR
EE
ITH
ER
t3d
B/O
CT
AV
E)
Wrj.
[(f~
-f,
)+
(fz)
ll%(f
df2)
11-’
W..
(LE
VE
LA
DJu
ST
ME
NT
FA
CT
OR
)’WO
Wo=
(gm
,)’w
o
Tlil
SS
PE
CT
RU
MIS
FO
RU
SE
ON
LVW
ITH
WIN
G.
MO
UN
TE
D
AN
DF
IN.T
lPS
TO
RE
51N
TH
ER
AN
GE
OF
q<2
501
bV\q
.ft
AN
DM
AC
HN
UM
BE
Rs0
.4S
.
rV~
=lf,
/f])(
f~-f
,)●
(o.5
)(f]-
f?W
])+
(fo-
f3)l”
’
w,=
(f~
/fj)w
lJ
W.=
(LE
VE
LA
DJu
ST
ME
NT
FA
CT
OR
)?W
o=
(g,~
,)’
Wo
WI
=(L
EV
EL
AD
JUS
TM
EN
TF
AC
TO
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MIL-HDBK-781
Pref, m,narv operational destq? requirements (expec:ed
I,fe of 5vears) (Cont,nued)
INDuCEDTHERMAL
FLIGHT EVENT
EXTERNAL INTERIOR
COMPARTMENT
LOCATION
RAOOMEPAYLOAO (FWO)
PAYLOAO (AFT)RECOVERYFUEL TANK
FMS
FAIRINGSFINS
ACTUATOR
COMBUSTOR
SURFACE
rc)
I
VIBRATION(ALL 3 AXES)
421
357329
366360
393
382382
NIA449
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132143164,q~
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N/A2t16
NIA
1
FLIGHT EVENT
CAPTIVE FLIGHT VIBRATION (INPUT)20-l SOHZ 0.0120~lHz-.
150- S00 Hz + 3dBJOCTAVE
500- 1s00 HZ 0.04g2/Hz
1500-2000 Hz - 3dB/OCTAVE
OVERALL: 8.24 9.m,DURATION: 1 HOUR PER AXIS
FREE FLIGHT VIBRATION (INPUT)
(FORWARD OF INLETS)
20-500 Hz’ + 3dBlocTAvE
500-2000 Hz 0.0Eq2/Hz
OVERALL: 11.8 9rrn\DuRATION: 2 MlNs. 15 SECONDS
(AFT OF INLE?S)
20-2000 Hz 0.43 gVHz
OVERALL: 29.2 9rm,
DURATION: 2 MINUTES
1 139
I . ..—. _____
MIL-HDBK-781
TABLE J I Life cvcle environments
U.’a. NAVYAN EXAMPLE
SUMMARY CHARTS FOR THELOGISTIC LIFE CYCLE
ENVIRONMENTSFOR A
LIFE OF 5-YEARS(43800 HOURS)
SUMMARY OF
STORES LIFE 12!>TRIBUTION (S-YEARS) IN MAJOR LIFE CYCLE PHASES
1. FACTORY/DEPOT REWORKHOLOtDELAY
IN. ROUTE MOVEMENT/ AND DuMP
STORE TRANSPORT HANDLING HANDLE STORAGE/MAINT STORAGE
(5 YEARS. HOURS HOURS HOURS HOURS HOURS
43800 HR51 ~ (~~~ (PERcENT)
AN ExAMPLE 1667 809
(3.81) (1.85)
ITEMNUMBER
1.2.3.4.5.6.7.8.9.
10,
SPECIFIEDEQUIVALENTAMPLITUDE~3-AXES,with excePIIon)
35G30G25G3SG (LONG);;: (VERT)
25G30G1 FOOT DROPON CONCRETE18 INCH DROP
6120 35141
(.:) (13.97) [80.23)
NOMINALDURATIOFY
llmsIlmsIlms18 ms
6 ms2 ms
Ilms10m5
MAXIMUMPROBABLENUMBER
ON CONCRETE{EDGEwISEDROPS)
3. TRANSPORTATION VIBRATION (SINE) -- LOG SWEEP RATE (ASSUME())ESTIMATED
ACCELERATIONITEM LEVEL
NQ&x&?~
1, 12. 1
3. 2A 35 s
ASSUMEDFREOuENcy RANGE(Hz)
2-5s-lo10-20
20-6060-500
6
;244143
1
CAPTIVEAND FREE
FLIGHTHOURS
~
22.68
(.05)
STORE
STATUSCONDITION
1
2s
:6661
2
VIBRATION ESTIMATEDDURATION DuRATION STORETOTAL IN-RESOURCE STATUS[HOURS) (MINUTES) CONDITION
3.0 30. 1
2.3 28. 1
2.3 2B. 1
3.6 33. 1
7.0 48. 1
140
TABLE 51. Life cycle environments (Continued]
U.S. NAVYAN EXAMPLE
SUMMARY CHARTS FOR THELOGISTIC LIFE CYCLE
ENVIRONMENTSFOR A
LIFE OF 5-YEARS(438oO HOURS}
(CONTINUEO)
4. CAPTIVE FLIGHT VIB~TION (WNOOMJ - POWER SPECTRAL DENSITYNOMINAL AVEWGE
FLIGHT
LIFETIMEPERCENT SAFETY EFFE~lvE DuF@TION STORE
ITEM CONDITION MISSIONS FACTOR MAXIMUM EXPECTEO STATUS
NuMBER FOR STORE EMPLOYED ON q-LEVEL P5D (q2/Hz) AT MAX. PSD CONDITION
1. MEAN 8S.0
2 MAX 9 1.5
3. CLIMB/DESC 9.04. DIVE/PULLOUT 2.5
5 HIGH BuFFET 1,0
6 T.O./lANDlNG 1.0
7. FREE-FLIGHT 100.0
5 TEMPERATURE . HUMIDITY
1601401201007032
0- 2s-45- 6S
(70.1)
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- 53.9)
1.51.5
1.5
1.5
1.51.s
1.0
6. ACCELERATION (SUSTAINEO FREE FLIGHT)
MAXIMUMITEM LEvELNuMBER (9)
1. +31.02 -4.0
3 + 12.04 -12.0
REwTIVEHUMIDITYPERCENT
2031do47
4943342s16
3
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0.090 1.5 M#n$ 5
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0.291 l. OMins 5
0.023 1.0 M(n% 5
0.200 4S8.0 Sees 6
PROBABLEOCCURRENCE TIME
OURATION~s
20.293.
1720.S367.8163.
843.229.
38.4.1.
STOREDIRE~lON STATUS
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LONGITUDINAL 6LONGITUDINALRADIAL 6RAOIAL 6
141
-. _=.,,- . .-- .,-. . . . .. . .. .. . ..
.
MIL-HDBK-781
7 ALTITUDE
8 SALT SPRAY
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I 2
9 ACOUSTIC
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1.
2.
3.4.
TABLE51 Life c@eenvirOnments( Cmmtnued)
U.S. NAVYAN EXAMPLE
SUMMARY CHARTS FOR THE
LOGISTIC LIFE CYCLE
ENVIRONMENTSFOR A
LIFE OF SYEARS(438oO HOU RS)
(CONTINUED)
MAXIMUMALTITUDE[FEET)
3s000.>40000.
>30000,>20000.
5000.
MAXIMUMALLOWABLEEFFECT
MAxIMUMPROBABLE 5TOREDU RATION STATUS FLIGHT
JTIME) COND ITION EMEYL
17. Hrs
1. Hrs
5. Hr$9. Hr\
33. Se<
ALLOWABLE cORROSION 50.
LEVEL EQUIVALENT TO0.007 INCHES OF HOTROLLED STEEL DISSIPATEDPER 5 YEARS LIFE CYCLE.5AME, EXCEPT 0.001 IN. 5.
ASSUMEO
MAXIMUM FREQuENCY
LEVEL WNGE
MB O VERALIJ Wz)
110 20-20000120 20-20000160 20-20000
163 20-20000
1,2 AIR FREIGHT
5 CAPTIVE FLIGHT5 CAPTIVE FLIGHT
5 WPTIVE FLIGHT6 FREE FLIGHT
OIRECTEXPOSUREOURATION STOREEXPE~ED STATUS~DAYS) CONDITION
1,3,4
2,5,6
MAXIMUMPROBABLE
DuRATION[TIME)
33. Hrs
9. Hrsl.Hrs
w. kc
STORE5TATUS~NDITION
1
256
142
MIL-HOBK-781
TABLES1. Lifecvde environments (Cominued)
us. NAVYAN EXAMPLE
suMMARy CHARTS FOR THELOGISTIC LIFE CYCLE
ENVIRONMENTSFOR A
LIFE OF S-YEARS(43Eo0 HOURS)
(CONTINUED)
ITEM
1.
2.3.4,
ITEMNUMUR
1.
2
3.4.
12. ~ IT
1
2.
EXPECTEDMAXIMUMLEVEL(lN/HR)
2
22
2
EXPECTEDMAXIMUMLEVEL(INIHR)
10
1010
10
MAXIMUMPROBABLEDURATION
80. Hrs1. Hrs
3. Min
160. Sec
MAXIMLJMPRO.9ABLEDURATION
64. Hrs1. W%
2. Min128. Sec
MAXIMUM MAXIMUMPROBABLE PR08ABLEJJvfi gJQgJMJ
45 MPH WIND 38. Hrs0.001 TO O.12SINCH
DIAMETER PARTICLE S12E
SAME }.Hrs
STORESTATUSCONDITION
1
25
6
STORESTATUSCONDITION
1
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56
STORESTATUS
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NOTES TO ACCOMPANYU S NAVY STORES LOGISTIC CYCLE
OURATION ANO LEVELS OF EXPOSUR[7Ci EtiViKDNK4ENiS
so!? .4 I.!FE OF 5. YEA!?S (43S00 HOURS)
GENERAL - NEGLIGIBLE RESPONSE CONDI rlONS ARE INDICATEO BY A DASH. STORE STATUS DEFINITIONSliOWN IN ACCOMPANYING CHART TO NOTES (STORES LOGISTICS STATUs CONL)ITICIN.
NOTE U)
- .A5 MC IS AIRB.ASE OR .A!RCKAFT CARRIER
“ - ASSUMED ENVIRONMENTAL LEvEL
““” -ASSUME EACH TAKEOFF lSA~TAPULT, EACH LANDING AN ARRESTMENT
A- 25g FOR 11 TO 18 MILLISECONDS (LONGITUDINAL)1 FO13T OFiOP TG CUFJCRETE (CGRNEE L3Rofi](AS5L!F. !E!.! AX IP.!L! !.! c! ! !JCCL!!?RE!!CE PER 6 EVENTS! 5 YEARS)3.5g FOR 2ST0 50 MI LLISECONDS(VERTlaL AN DLATEFLAL)(ASSUMED4 OCCURRENCES PER EVENT/5 YEARS)
6- ]gihuid 1 HZ TO lUHZ2g FRG?wI I!JHZ TO 2CHZ3g FROM 20Hz TO 60HzSg FROM 60 ~Z TO 500Hz
C-25g FOR 11 TO 18 MILLISECONDS (EACHAXIS)1 FG07 DROP 70 CGNCRETE (COiiNt R unum)
------
(ASSUME MAXIMUM OF 1 OCCURRENCE PER6EVENTS/5YEARS)
0- ASSUMED NOMINAL LIFE LOADING/UNLOADING EACH TWO FLIGHTS(2 HOURS LOADING AND 1.5 HOURS UNLOADING) AND NUMBER OF FLIGHTS(AVERAGE 1.50 H6u RS/FLIGHT)
.A.!VROXIM.ATE NOM.IWM TOTALMISSILE NAME NO LOAOSLINLOADS FLT. liOURS LD/UNLD HOURSAN EXAMPLE -1 22.s0 23
E -THE APPLIIMEILE MISSILE BUFF ETfiHOCK LEvELS (COMBAT MISSIONS) ARE 29,~,(LO:JG:TLIDINAL) &5cj,~, (VERTlCALA?:D KT:RAL) 10 HZT060HZ; ASXIMED)
154
TABLE S1. life cvde environments fCOntinWd)AN EXAMPLE
NOTES TO ACCOMPANYU.S. NAVY STORES LOGISTIC CYCLE
DUWTION AND LEVELS OF EXPOSURETO ENvIRONMENTS
FOR A LIFE OF 5-YEARS ( 43.900 HOURS)(CONTINUED).
F - SEE APPLICABLE MISSION PROFILE(S) FOR UtPTIVE CARRIAGE FORA-6 P-3FIQF-4 Dc- 130F/A- 18
NOMINAL UPTIVE FLIGHT VIBIWTION LEVE13 (ASSUMEO)
[FOR SPEC!FIC STORE FLIGHT HOURS, SEE INDIVIDUAL STORE DURATION ANCI LEVELS OFEXPOSURE TO ENVIRONMENTS.)
0.024 9UHZ, 20 TO 2S0 Hz0.004 gZ/liz, 2S0 TO 1S00 HZ0.012 gl/Hz, 1S00 TO 2000 HZ (MEAN CAPTIVE FLIGHT)
0.096 92/Hz, 20 TO 250 Hz0.016 gzltfz, 2S0 TO 1S00 HZ0.048 g2/Hz, 1S00 TO 2000 Hz (lNTERMl~ENT MAXIMUM)
BUFFET LEVELS (ASSUMED AT 1 PERCENT OF FLIGHTTIME)
IOHZ - 30tiz0.1 gVHz30 H2 - 200 ~Z
-6 dB/OCTAVE
G - SEE APPLICABLE MACH NuMBER VS. ALTITUDE FOR RECOVERY TEMPERATURE ANOMISSION PROFILES OF APPLICABLE CARRIER AIRCRAFTA.6 P-3F/OF-4 DC-130FIA- I B
H- lSg 11 TO 18 MILLISECOND (ASSUME0.40CCURRENCES/ 10 UNLOAOINGS)18 IN. OROP TO CONCRETE (EDGEWISE OROP)(ASSUME 1 OCCURRENCE PER 10 UNLOAOINGS)
I - ASSUME 12 HOURS EACH FOR STORE ASSEM8LY/DISASSEMEILY AND MAINTENANCE.
MAINTENANCE. INSPECT, TEST.NOMINAL ANNUAL ANO ASSEMBLY/DISASSEMBLY
MISSILE NAME FREOUENCY ASSUMED (HOURS)AN EXAMPLF 6 SB4
J - ASSUME 1 SHOCK EACH 1 HOUR AND 30 MINUTES IN DEPOT ANDASSEMBLY/DISASSEMBLY AND EACH 4 HOURS HANDLING TRANSPORT AND TEST
155
MIL-HDBK-7B1
TABLE 51, Life cycle environments (Continued)AN EXAMPLE
K
L
NOTES TO ACCOMPANYU.S. NAVY STORES LOGISTIC CYCLE
DURATION AND LEVELS OF EXPOSURETO ENVIRONMENTS
FOR A LIFE OF S-YEARS (43S00 HOURS)(CONTINUEO).
ASSUM1” 1 OAY FLIGHT LINE sTomGE PER 4 FLIGHTS, RUOY/ALERT 4 HOURS PER FLIGHT, AND LIVESTOPAGE AT ONE DAY PER LOAO/UNLOAO. AS FOLLOWS
LIVE FLIGHT LINE READYMISSII E NAME STORAGE STOFLAGE ALERT
y y @#iiii-Exx~
ASSUMING OELIVERY. EMPLOYMENT. AND REPAIIUREWORK LIFE FREOUENCY. THEN TtiEREMAINING PORTION OF LIFE SPENT IN DEAD STORAGE
TOTAL TOTALRECYCLE CONUS RECYCLE TO DLJRATION LIFE DEAD
MISSILE NAME FAnORY/OEPOT EUR DEPOT IN ACWE STOWGEIN DAYS IN OAYS STATUS IN DAYS
(PERCENT) (PERCENT) IN OAYS (PERCENT)(PERCENT)
AN EXAMPLE 265.—.. - . .
145 363(14.S2) (7.95) (2.87) (7:.68)
M - SEE INDIVIDUAL STORE LISTING FOR QUANTITIES
N - VIBRATION (RANDOM) ACCELERATION SPECriWL DENSITY LEVELS FOR ALL STORES IN FREE FLIGHT(ASSUMEO)
NOMINALRANDOM VIBRATION (gZ/Hz) FREOUENCY
LAUNCH ~ FREE FLIGHT ~
0.024 0.01 0.006 20-2500.135 0.08 0.02s 2s0 -15000.012 0.02 0.003 1Soo -2000
APPROXIMATE MAXIMUM FREE-FLIGHT EvENT TIMES (IN SECONDS)
MISSILE NAMEAN EXAMPLE
SAFE AND ARM FREE-FLIGHT9.10 16S.00
mFREE-FLIGHT
.
FUSING ASSUMEDAT 5.20 SECFROM lMPACl
156
MIL-HDEK-7E4
I
I
o-
EVENTNuMBER
1
23456789?9tl121314is~~
171819>02122232A
TABLE 51. Life Ode ●nvironment%. (Continued)AN EXAMPLE
NOTES TO ACCOMPANYU.S. NAW STORES LOGISTIC CYCLE
DURATION AND LEVELS OF EXPOSURETO ENVIRONMEN~
FOR A LIFE OF $YEAR5 (43800 HOURS)(CONTINUEOI
STORES.- -ijfi c-> --.. -.+ -.s5iATii5 Lvlw”, , i“lws
STATUSCONDITION”
111
I136,!
111i:11111
;>=,.,, ”111
STATUS CONDITION
1, INOPERATIVE IN CONTAINER2. INOPERATIVE OUT OF CONTAINER
WENT STATUSUUMBER CONOITION”
~25 32627 2~~ ~
29 s30 231 3, A32 233 g
34 23s 236 2
536 239 240 541 242 243 b44 6
L
45 646 647 642
3. VISUAL, DESICAN7, HiJMiDITY (iNCFEiA7iVE IN CONTAINER;4. lNOpERATIVE - CONTINUITY/BIT (lN/OUT CONTAINER)5 PARTIALLY OPEFUTIVE6: FULLY OPEtiTIVE
157
—.--, . . . . . . . ,.%_J ..--..,4
MIL-HDBK-781
TABLE 52 A$wmed Ivoical attack mis$ion mofile~
_
MACHNUM-
BER
w
:S”:AN.DARDDAY)
r64614949691B62291862291E549
76436
ION [2 HOURS. 10 MINUTES)
EVENTTIME(MIN-uTES)
=
NC)ISTO3AY)
SVENT
wM-BCR
01
1
3456789
101112
Tn(”c)(HOTDAY)
056 OAY
TR(”C)(COLDDAY) IALTITUDE
(FEET) 10% OAY I REMARKS
-1515251s
242227
232310
0.01,000
30,0008,0003.000B,0003,0000,0003.0005,000
47,0004,000
0.0
0.00.6730.5820.6720.8320.7520.8320.7520.8320.6680.6190.5840.0
1536
-3 I21442744.’74427
-422415—
4568
t4877 ~’5577 !’5577 !’57
-145545
-54 GROUNO RUNUP/lAXl-35 TAKEOFF/CLiMB/RU N-OUT-53 CLIMBJCRU15E-13 DESCEND/ON-STATION-23 OIVE/ATTACK
-8 CLlM8/LOITER-23 OIVE/ATTACK ‘
-8 CLIMBIRECONNOITER-23 DIVE/ATTACK-23 CLIMB/DEPART STATION-55 CLIMB/CRUISE (BACK)-33 OESCENO/CRUISE/lAN OING-54 TAX1/PARK
HIGH-MEOIUM-LOW MISSION (2 HOURS, 10 MINUTES)
vENTrlMEMIN-JTE5)
-157
184628
1613
324263
197
10
-... .–—1P,($C)(HOT
TrJ-C)(COLDOAY)
O% OAY
vENT‘JuM-BER
TALTITuDE MACH
(FEET) NUM.
BER
0.0 0.05,000 0.45
30,000 0.6510.000 0.8520,000 0.8010,000 0.9220,000 0.7010,000 0.65
1,000 0.705.000 0.6S
500 0.932.000 0.80
[ST%N.OARODAY)
“d-cl(STDDAY)
OAY)
10% DAY REMARKS
o1
234
56789
1011121314151617
0249
186736436B6233A430700520
1.263881
1,055417960430401
0
1s16
-2730
4
36-3
-1638265843512647162415
4543
558216413427\56937685S881425545
-54-33-50
-8-28
-3-34-21-33-30-19-26-25-40-26-21-39-54
GROUND RUN UpfiAXITAKEOFF/CLlM8/LOWCRUISECLlM6/ON-5TAT10FJDESCEND/HIGli ATTACKCLlM8/LOITEROESCEND/HIGH ATTACKCLIMB/LOITEROESCEND/HIGH ATTACKOESCEND/ON-STATIONCLIMB/lNITIAL RUN-INOIVUAnACKCLIM81RECONN01TERDIVE/Al_TACKCLIMBIRECONNOITEROIVE/AT_TACKCLIMB/CRu15E(BACK)DESCENO/CRU15E/L_ANOINCTAXUPARK
I.1
5002.0001,000
10.0003,000
0.0
0850.550.B20.650.550.0
J/ OR MAXIMUM AS AVAILABLE [NOT LES5THAN 71oc)TR - RECOVERY TEMPERATuRETR ~R) = T- ~R) [1 + 0,178 (MACH No )?]
i
158
FE.C
YCLE
/EN
T{S
EEG
uRES
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—-
IA,
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pt,v
e
TABL
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m{
.—-=
RELl
A81
LlTY
.DEF
\N
EOTE
KiT
EVEN
TSFO
RA
IR.ll
RfD
MIS
SILE
SA
ND
AS$
ENIB
LED
EXTE
RNA
LST
ORE
SF1
70M
OPE
RAT
10N
A1
LIFE
CYC
LEEN
VIR
ON
MEN
TAL
REO
IJIR
EMEN
TS(S
EETA
BLE
51)
GRO
UN
DFI
RE/P
OSL
F~
NoN
OPE
RATI
NG
OPE
RATI
NG
(SEE
FIG
URE
130)
.—C
APT
IVE-
fLIG
HT
MIS
SIO
NS
HIG
H-M
EOIU
M-I
.OW
H1G
H-1
OW
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RE12
0)
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1)
THER
MA
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hfi8
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EEFI
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ES13
0AN
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1)—
——
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LSFO
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TEST
llEh
)hl
~dIo
rcal
cula
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)
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L[H
EDIJ
LED
,FE.
CYC
LEoC
CU
RR
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CE
S
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CA
TED
OR
TEST
YCIE
:vEN
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ICEN
TAG
IIIS
IRIII
UTE
D)
—-
40 (50)
(50)
ALL
OC
ATE
DTI
ME
INIA
CH
TEST
CYC
LEPE
RO
CC
URR
ENC
E(D
ISTR
IBU
TE)
——
. 25M
IN
(12,
sM
IN)
(12.
5M
IN]
-——
- 2ho
urs
(14M
!SSI
ON
Q
(16M
ISSI
ON
S)
3M
IN
(4M
ISSI
ON
S)
6MIN
$[C
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6MIN
5(FF
)
—-
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TOTA
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UM
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FEV
ENT
OC
CU
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CD
URI
NG
1[S
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LE—
——
.
7
——
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6
——
—-
6
Or
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ENT’
PER
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AD
JUST
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EvEN
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STIT
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CYC
LETI
STA
ND
TIM
EFA
CTO
R
0F2.
03@
(~x2
.03)
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STIT
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OIJ
R5
5PEN
1IN
EAC
HEv
ENT
DU
RIN
GTO
TAL
TIST
(O
XQ
X1O
.——
[r.——
2.91
7SO
MIN
59.2
146
SEC
:(2
5MIN
(OC
CIJ
RFIE
NC
E23
SEC
)70
TIM
ES)
(25
MIN
235E
C)
.——
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4H
RS24
4.0
4M
lhl
(36
MlS
S10N
!i)(O
CC
URR
ENC
E60
TIM
E5)
(24
MIS
SIO
NS) u-——
————.
0.3
6M
IN6.
16
SEC
(6M
ISSI
ON
S)(O
CC
URR
ENC
E60
TIM
ES)
-——
——
——
0.4
12M
!Nlb
.24
I ❑A
I ~
I Elc
I ElD
~
(Comlrwd)
A MINIMuM OF FOUR TEST ITEMS AT 325 HOURS OF TESTING PER TEST ITEM ITHAT IS NOTLESS THAN 1300 HOURS OF TOTAL TESTING IS RECOMMENDED).
THE TEST CYCLEffIME FACTOR IS DETERMINE BY DIVIDING THE TOTAL TIME ALLOCATEOPfR TEST ITEM BY THE TOTAL T:ME PER TEST CYCsf ‘>3-C, <C0!7 = 28.29!, OR 2.03 Ti:.!E,_ .> ,“.ADJUSTMENT FACTOR FOR EACH TEST EvENT FOR 10 nCLES).
uSE TO ExpANDTtiE PROFILE TIME SCALE OF FIGuREs 143 THnouGH l* AND THECORRESPONDING TABLES (THAT IS, 2.03 TIMES EACH MANEUVER DuRATION FOR TESTINGIN EXAM.Lt mu, tLES).- .“--. ,
ONE SIMU~TEDMUNCH PERTEST ITEM (ASSUMED 32 SHOURSCAPTIVE FLIGHT/ lAUNCH)
SEE S.9.3. 1 FOR SCHEDULING SHORT-TERM AND LONG-TERM ELECTRl~L INTERRuPTS.
160
M!4-HDBK-781
*.& R, al a
2
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- =1
I
m w
TABL
ESS
,A
num
ed
fn?e
.flia
htrn
iwo
nPr
ofil
efo
r●
xanw
hst
ore
(Io
w.lo
w),
vib
rdtio
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—
SE
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EN
ER
AL
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EE
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GH
TN
OT
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EX
TP
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PRES
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ENTS
IA
NO
2A
RE(q
)=
9250
lbvf
t~FI
NA
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ALU
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FA
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$TEO
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(OvL
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LLY-
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AT
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MIL-HDBK-781
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1.
TABLE 55. Assumed free. fliaht m,s%;on profile for example store (Iow.low). vi brat, on (C.antanued)
GENERAL FREE-FLIGHT NOTE
Based on the approximate relationship of a constant baundary layer presure ratio with flight
dynamic pressure> and aerad ynamicall y-induced random vibralion (Ref erence 23. paget 21 and S8) and therelationship of WO = K(q)l (the $peetncm relatiomhlp between ●quipment Iaeations and surface
diicontinuities), the free-flight (g,~,)z acceleration. (hence. the kvel relationship for the P5D vemusfrequency) is assumed to vary in direct proponion to the jet aircraft $maath wtiaces flow and d,scont,nuity
wrface$ flow coefficients.
K [smooth) K [free-fliaht)
K (discontinuity) = K (captive-flight)
0“ [w,] - K (smooth) (WO) Captive = (0.1914) Iwl)]free - K (dtscontunuity)
high speed
flight captive PSD
when?:
Q(M = 0.45) SqSq(M = 2.0)
and,
W, = WO-3dB
These limits are ba$ed on Reference 23, pages 21 through 25 and the initial aswmptioni of the
MS O.45 and q= 2501 bs/ft2 the mmlmum level af WOfartecting.
then,
19fmi(q, ‘0)1 = (o. 1914)2 [g,m, (q, W,J]free high speed
flight captive dataar.
[g,fmkf# Wo)l = (0.4375) Ig,m, (q. w~)]free high speedflight Captive data
where,
the g,~, relationship is shown in FIGURES 132 through 134q(MIN) s q s 5930 Ibtiftz
qMIN islis{ed in TABLE .tBfor FIGuRES 132 thru 134MACH (MAX) = 2.0V- = 1116.89 fv!econd. (for Mach = 1.0 at sea level)
q(MAX = 5930 Ibvftz (for Mach = 2.0 at sea level)
163
TA
BLE
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NIA
Accept-reject cri~eria
!/Total test time is the summation of operaung time of all units included in test $ample?~To determine Ihe actual termination tome, multo ply the standardized termination Ume (1) by the 10Wel teSl
MT8F ( 8,).
FIGURE 9 Test Plan l-D.
188
MIL-I+DBK-781
OC CURVE
.
fEiEa=la = 10 percent~ : p5Pyrcent
. .
{o~’’’’’I’’’’’ ””’’’’’”” ‘“ )
1.0 2.0 3.0 e“
ExPD3RI~ TIhfE CURVE
20
i~I
i6 I \
14I
12~ I \
10- ,
8. / \ 1~.- /’
4 /
o1.0 2.0 3.0 00
1.0 e. 4.5 e;1
TRUEI’i’fmExwmm AS KULT!FUS eo, el
FIGURE9. Test Plan I-D, (Continued)
i89
MIL-HDBK-781
Decition Risks (Nominal) 20 PercentDt$crimination Ratio(d) 1.5: 1
I
-.———
.——
——
ChargeableI
failures
0,
09
REIECT
/
/CONTtNUE
TEST
tandardized termination time, t ?’
T
Rejecl at ~s Accept al 142
8.76 16.359.98 17.57
11.19 78.7312.41 19.9913.62 21.2114.64 21.9016.05 21.9017.28 21.90lEI.SO 21.9021.90 N/A
Accept-reject criteria
II TCIIal IeSt time ij the $ummat, on of operating time of all unil% included in te$t Sample
2) 10 determ, ne the actual term( natton ttme, multtply the standardized terminatmn Ilme (I) by the lower IeslMTBF( 8,)
FIGURE 10 Test Plan II-D.
190
I
5 10 ?5 10 25
TOTAL TEST TIME (IN MULTIPLES OF LOWER TEST MTLIF, &l) Y
tandardized ter
Reject at (ns
NIANIAI(IA
.241.462.673.90S.126.337.55
nation time. t ?I
Accept at tA z
4.195.406.627.839.05
10.2611.4912.7113.9215.14
Chargeablefailures
)
In
.
EMPE
CTE
OTE
STT[
ME
EXPR
ESSE
DAS
MUL
TIPI
.ES
OF
130
1
P!?O
BABI
LITY
OF
ACCE
PTAN
CE
0
0 “1a).
*.
0 N “0
DI,
J
&o
mm
,-4
~
..
r \
ann
.-w
..0
0 :.3n
-mm :: m
m3>
““
CLm
o
MIL-HDBK-781
I
Decision Risk$ (Nominal) 10 Percent
I
Di$cnmina[,on Ratio (d) 2.0:1
10
1s
5
5 10 15 10 15
TOTAL TEST TIME (IN MUL7TPLES OF LOWER TEST MTBF, 8,) !~
o
I Chargeable Standardized termination time, t?,
failures Reject at tgs Accept at t, 2
0 N/A 4.40N/A 5.79
; WA 7.183 .70 8.S64 2.08 9.94
3.46 11.342 4.86 12.727 6.24 14.108 7.63 15.49
Accepl-Re1/ TOtal test time i, the ~“mmatiOn Of Operatinq lime c
Chargeablefailures
91011121314Is16
I criterta
landardized termination time. t ?
Reiectat 1A5 I Acceot al 1.2
9.02 16.8610.40 18.2611.79 19.6S13.18 20.6014.56 20.6015.94 20.6017.34 20.6020.60 NIA
MTE$ ( 8,).
FIGuRE 1 Test Plan II I-D
192
.. -
EXPE
CTED
TEST
TIM
EEX
’PRC
SSED
ASM
ULTI
PLES
OF
00
.-Ll
PRO
IIAB
ILIT
YO
FAC
CEPT
ANCE
..
.‘&.
bl”o
,uco$
,,,,,,,,,
,,,,!,,
,,,!_
___,,,
,,,,,,,
,,,,
,,..,.
.,,,,,
,,,,,
.,
..
..
P_...-
\.— r .——
_—\ —\.—.—
.—~uU.<
\—+
—.
‘\,—.
—-.
..
m“
—.
\——
__..
t#lL-HDBK.7Sl
I
1’
a = 20 percent
B = 20 Percentd = 2:1
OC CURVE1.0
.9 i
.6
.7 f
.6/
!.5
.4 /“ 1
,3 /
7 /. .
.1i
o J:. Il,trml,t!1.0 2.0 3.0 90
1.0 @i 6.0 Q1
TRUE HT5F W%ESSEO AS W!LT!F’KS OF 9., Qi
EXPECTEDTEST TIW CUR.VE?.4
L2.2 -
[ I\ ~-.i
2.0 /
1.8 ,, -
1.6 -1
1.4 1
~.~ 1
1.0i
.Br I
.6 I
.4 t /
.2 },/I
, I,
1.0 2.0 3.0 00
1.091
TRUEMTBF EXPI?ESSEII AS WLTIPLES ‘F ‘Qt ‘1
FIGURE 12. “Test Plan Iv-o. ( Continued)
195
!4!L+99K.781
oeCl$i L!~! Risks (Nominal) 10 Percen:Dl$clilninat,on Rati~(d) 3.0:1
‘ r —-–~-—
I~ ~
[
6’–—
.—
D&l~~
—..
____ 1-’”I ACCEPT
.—
— t,~na “,/ 10I MICF . @,
.-La . v
TOTAL TEST TIME (IN MUL77PLE$ OF LOWER TEST MT’BFJ @:)!/
WANIA
.572.223,875.527.17
IQ.qs
I Chargeable Standardized termination time, t 21
failures
r’ ‘eieda”n’ ‘ “’’”’””-2 ‘23a561
~,?~
5.407.050.70
10,3510.3510.35N!A
Accept-reject crit.prla
Lr TOtaI test t,me is the summation of operating lime of all units included in test Sample.
Y TO determine the ZCWd ierfninalion the. rnuliipiy the standardized termination time (t) by the iower testMTBF( C?:).
FIGURE 13. Ten Plan V-D
196
. . . . . . . .
A6!L-F!9BK-7M
OC CURVE1.0.
.9t
.6 ~
.7 /~
.6/
1.5
.4 /
.3 /
.2 I
c . :~ percent
B = 10 percent
d= 3:1
.It / I 1
ot’~,’’’’’’’’’’’’’’’’ l’” ““d1.0 2.0 3.0 ‘aO
1.0 ei 9.0 Q,.
--- -. -- “
TRUE MTBF EXPRESSED AS WLIIPLD ur WOI al
1.4 I J
1.2 / I
‘!~j ....,,.1.0 2.0 3.090
:.891 9.091
TRUE MTBF EXPRESSED AS MULTIPLES OF 9., ~1
FIGURE 13. Test Plan V-D. [Continued)
197
MIL-HDBK-7B1
&ci\ion R%kt (:icmiinal)Discrim,natton Ratio (d)
3
1
——-——
7-
.—
..— — ——
)%%E.pe.eddecisi.. @.t
/
b MTBF . &
I
.75 1.50 2.35 3.00 3.75 4.s0
ONTINUETEST
——— .
L
.—.
TOTAL TEST TIME (IN MULT3PLES OF LOWER TEST MTBF, @t)IJ
ijl WA.1-4,32.36 4.50 1
4.50 NIA
~
Accept-reject Criteria
~1 T~Ial ,e~, time ij the ~“mmatiO” of OperatinQ [i me Of all “nit$ in~l”ded i“ test mmDle
!5
~1 TO d~termin~ the aCLUal Ierminat!on ttme, mul[cply the standardized Iermmal(on urne (1) by the lower les!
I
MTBF[ til).
FIGuRE 14. Test Plan Vi-D
198
..
-..
.
EXPE
CTED
TEST
T“(M
[E’
KPRE
SSEI
)AS
MUL
TIPL
ES(IF
90
0 10“ N 0“
k.
PRO
BABI
LITY
OF
ACCE
PTAN
CE
0“1
., -,(
MIL-HDBK-781
Deciwon RMs (Nominal) ;G %,cemOiscrim; na?ion Ratio !d! 1.5:1
6
r
——
5/ 1
RLIEff Y
I
III
galCuu+rp-..-.... I “
1
I<u IIn.:3
/I
%z
1/
tt I
ACCEPT
]
I
~ / I
1 1 3 ● 5 6 7
TOTAL TEST TTME (IN MULTIPLES OF LOWER TEST MTBF. &)LI
I
I
200
w 0
...
z! g xl m,
EXPE
C”TE
IITE
STTI
ME
EXPR
ESSE
DAS
NULT
lf’LE
sO
F‘o
.?0-
c>:
[. “0 S’
- “0,,
1 !.OF
ACCE
PTAN
CE
,4.
..
“Llm
”wa)
w”o
\
1 \
i
MIL-HDBK-781
Oecision Risks (Nominal] 30 PercentDiwriminat,on Rauo (d) 2.0:1
3
r
—.—--?-
REJECf
2’I
3
~CON#IE
Y
2
~
$t
E.p.cwd de.ision ~.t
1,0 1.0 3.0 4.0 5.0
TOTAL TEST T3ME (IN MULTIPLES OF LOWER TSST MTBF, (17$),
mStandardized termination time, t v
Accept-reject Cmeria
11 TOWII test time is the summation of Operaling time Of ail uniL$ included in test sample.ZI TO determi ne the actual termination time, multiply the standardized termination time (1) by the lower KeSt
MTBF ( 8}).
FIGuRE 16. Test Plan VIII-D.
202
I
I
I
1
I
I
.
(
Ez3=E=2I I I
.li / 1
EXPECTED TEST TIME CURVE
::~.9( i I I
I
.8r I Ir , i
I.71 I I , IL
K I I I...5 I
.4 / I ~
L.2 / I ! I
!.1 Io
# 11 1.0 2.0 3.0 ‘=’0
%
FIGURE 16. Test Plan VIII-D. (Continued)
203
Mii.-i-iimt-m
--.---Ut.IJkL 1
CCIW:WETEST
II
I
ACCEPT
IIII
I IATEST TIME !~lL;IPLES OF @i)
FIGURE 17. Fixed-duration test plan (examnle),
204
MIL-HOFEK.7FI
10°A CONSUMER’S I?ISK WI TEST PLANS
1yW&R
MT43F (C+o)FORPP03uZER’5RIW or
~ Ic% 0; 20”/. a~ 3W. a
8
TOTAL TEST mME ( IN MULTIPLES OF LOWER TEST MTBF. 8, )
Trsr PLAN NUMOCR OF 6AILUR[5 ToTAL TIST ttmc m ACCf?Ti6BLf 8 OISCR!MINRTIONRAIID. ( @a~t,) *ORNuMBfRs (MuL~/ts OF [MuLflE$Of
ACCEPTEDPR00L2CtR3 RISK
REJECTED a. 30V. a.zo~. a. 70..;
10.1 0 \ 2.30 230. 646 103: 11 8s
10.2 1 2 309 1.94. 3.54 472 7.32
10.3lo.d10510.610.710-810.9
>0.1010.1110-1210.1310.1.510.1510-1610.1710. IB10.1910.20
2
3a5678910111?13141516171819
3a567s91011!2
1314151617>81920
5326687.999.27
10.5311.7712991.i2,
1541
166017.781896?01321.19224$
23612475
25.90
1.77,167+1.59 +!.55 .1.s0 .147.143.1.d2.1.40.1.38.1.37.1.35.1.34.1.33.t.32 .1.3> .1,30.1.29 ●
1.9s!.9s1.061,80!.751,701,661.63I,to1,S61.S61.54)“52$.501,48
3 4?
2911591,213,122112 0?1 951.89!.04
\ .79
1.7s1.72
1.69
t .671,6>
1.62
1.60
4 B]
3833291701.702.S32391281192122.002001951911.87, Ba1 781.78
FIGURE 18. 10 Percent Consumer’s Ri$k (8) Test Plans
205
MTBF (XC31) ) r-
M::.-HDBK-78?
20% CONSUMZR’S RISK (p) TEST PLANS
--r-rT—
~
—
—
t
+
+y+~ , -#-
,4 ,5 !6 ,7 lB ,9
-+424
TC2TAL1”ESTTIME( IN MU LTIPLESUF LWMERTESTFJTBF, 61 j
20.220.3:..:
20.520.62G.720.820.9
A3.lc20-1120.1220.1320.1420-1 s20.16?O.! 720.1820.1910.20
1011
13
56789iil11121314IS16!?181920
2,994.18~,: ;
6.727.91S.aa
10.2311.381>.5213.6S14,7815.9017.0118.1119.23.T~.34
11.4411,5423.63
1.s0.1.83.;.:0 .1.14.1.32.1.; G.1.20.1.26.1.25.IJa.!.23 .1.22.1.21.12!.1.20.1.!? ,1.19,1,10.!.1s.
2.132.24:.921.051.75
i .6a1.621.s7
1.341.s11Aa1..61.44
1.381.371.3s
3.632.792,:02.172.03:.s21,031.771.771.671.641.601,s81.551.531.s11A97.Xa1.46
5.623.883.!s2.762.512.332.202.092.011.941.891.Ba1.801.761.731.7C1.611.651.63
FIGURE 19. 20 Percent Conwmer’s Risk (B) Test Plans.
206
1,
I
TOTAL TEST TIME (IN MULTIPLES OF LOWER TEST MlSF, 8, )
11s1 PLAN UUM8[R Of FAILURtS TOTAL TE5TT1MCIT) ACCEPTABLE~ DISCRIMINATIONRATIO. (&./6,l flOR
WM91RS [MUL~tS OF lMU;T~LM ?R032uCE71’SRISKAC(f~TEfi Ril F.7to ., g .jo:i 22 .20!’,
36.1 6
a . 10*;? xl 1.20. 3.37 535 ,,.~
30.2 1
30.3 230a 3?0. ~ 4
30.6 530.7 6?0.9 7
30.9 830.10 930!1 Ill
30.1 z 1130.13 12:0.!: !330.15 8430. tb 153$:7 1$,30-10 1730.19 18Jci.>c 19
234567891011121314is161710192C
>.a
3624,76s 89700a;;9.21
103011,39J2.47t3.s5ta.6z1S.69$676178198901996ZI 02?208
1.22.
1.20.1.19+!.s8 .1.17.
1.15+1.15.1.14.1.74.1.13,1.13.
;.:2+1.12.1.13+1.11 .1.11+~.11+;.l; .
1,10.
3.22\ .6;1.721.631.>51 w1 a61431.40! .38
1,361.2a1.331.311.301.29).>8~,::
1.27
2961 3:r 071911.751 711,65I 661,S61.331.’301.481 451 431,421.40339!.3s1.36
. .459~ ?g2.73243: ~~
20s1981.931,031.7a!.731.691,661 63I 601.581.5b, 5a1.52
I
207
MiL-ilCWK-78i
--.. -.--.,-.LUNt lUt-NLt
~O.OO LIhfITS
9.006.oi2?.~rJ
6.00~.q
4.00
3.00
2.00
].y
.80 — 702
.70 — 80%
I I I II I I I I I
.- I I
. ,,.30”
.201 2 34 5 678910 20 30
TOTAL NL04BER OF FAX LURES
FIGURE 21. Demonstrated MTBF confidence limit multipliers. for failure calculation.
208
___
c1 c :0 m ::
w o *
LOW
ERLI
MIT
.
MIL-HDBK-781
\
[\
Sfmdord f,xed-d. ratton tesf plan
J1
/Slonaord ti,ed-duration tast plan
/
=i!h :S:!; rejecl ior,
H
//
H
//
/ /
H. .
‘1\\\\\\\\
\7
mm~“w I 00 2.00
—S.oo
I4.00
TRUE MTEIF !1?4 MULTIPLES W LOWED TEST !tT~F)
PROGRAM WWs?G@S &IS[sSh!E:iT
FIGURE 23. Test Pian iX-b,
210
MIL-HDBIG781
1’
1.00
I.80 I
51
/.
Izz“
: ““l H
I
1.
-t Illz .doz
‘1
1/1sg
.20 I
~,~t
.Co.50 1.00 1.50 2.00 2.50 3.00
,00
.75 “1.50 2.25 3.00 3.75 4.50.00
TRU[ KTEF FxPR[SSED AS HULTIpLE oF oo.o~
FIGu RE23 Test Plan lX-D (Cononued)
211
MIL-I’(OBK-781
10.00I
.;tandmd fised-durutmn test plan
5000
‘Stondord lined-duration lest plonwith ●arly re)ac lion
25.00
20.00
15.00
5.00
0.00 I
— Early -occept testplan
0.00 Loo Zoo 3.00 4.00
TRUE MTBF (IN MuLTIPLES OF LOWER TEST MTBF)
PROGRAM MANAGER’S ASSESSMENT
FIG URE 24. Test Plan X-O.
212
PR
OB
AO
ILIT
TO
FA
CC
IPlfl
NC
E
-~
—
CL-m
o
kJIL-H02K-7al
,Skmdofd ftxeu kmlon Iesl plan
Ia.oo
2,00
0.00
\
\
\
\
\
\
\
\
\
tes! plan
0.00 Loo 2.00 S.oo 4D0
TFiUE fkiTBi (iN MULTIPLES OF L@VER TEST MTEF )
PROGRAM MANAGER’S ASSESSMENT
FIGURE 25. T~.
214
PR
oB?W
IILIT
YO
FA
CC
FP
TA
NC
[
“- o
-r—
.——
- ——
— —
——
-. .——
——
.——
.——
k‘--
i—
—-——
-‘-
.
‘i) —
—— ——
————
““’G!A =,,..W.W’..
‘Standard fixed -duratmn test plm
s -.$JU5 T // \ ,Early-accepf test plan
-0.00 1.00 2.00 S00 ● .00 s 00 6.00
TRUE MTBF (IN MULTIPLES OF LOWER TEST MTBF)
FIGURE 26. Tesl Plan XII-D.
216
:‘k
ma) c,
=.7—.
o.-
y“7
—.—
——
.——
.
——
..
—
—
——
..—
—-
——
——
.
o c> n c. x! .: m
O.m
o
IIII
II
,.,.
,..
MIL.HDBK-7BI
,.. S1CW3 t,aeo-dumtwn fesf Plot
‘--~
:)?s:
\
‘7
4
m 1,00 z .00 300 4.00 5.00 6.00
TRUE MTBF (IN MULTIPLES OF LOWER TEST MTBF)
PRCGfifiM MA NAGCR’S ASSESSMEN7
FIGuRE27 Tea Plan Xlll-D
z c1 c ,% . .
,.
Pllo
Bho
ILll
YO
fA
C([
Plh
NC
C
.— -. —.
—.
—. ,,
MIL-HDBK-781
S,arJa,3 lq. ea-~. ra!. on les, PI:}.5 :.= ./
w~fontioca fixed -d. rolto” test plor,7“001(x “ wltll ewly rejection
/ /‘“”;// \i \
moii7 \\/ //
1 H4.00 ~ / / ‘K
0.00c 00 100 2 m 3,w
~-. . {a ,C3 5.(XJ ~ ,00
TRuE MTBF (IN MuLTIPLES OF LOWER TEST MTBF!
PROGRAM MAKA~ER’s ASSESSMENT
FIGURE 2B lest Plan X.IV-D.
220
M! L-HRBK-7$31
gc CURVE
I
I
20 percent
zo percent
2.0:1
FIGu RE2B, Test Plan XlV-o. (Continued)
221
MIL-HDBK-781
Siondord fmed-durotra. I*sI pion
‘“ ~“–
/’\Svmutord h.ad-d. rotion test
with eorty reiecf ion
/F\\/\
“=t“ 1
1.00 z ,W 3,00 4.00 3.00 6.00 7,00 8.00 9,00
TRuE MTBF (IN MuLTIPLES OF LOWER TEST MTBF1
PROGRAM MANAGER’S ASSESSMENT
222
PF
!ON
MIIL
IIV
OF
AC
CIP
IAN
C[
ss’
— \ —..>
—.
——
0! c!--
1— J.—- .—— ,,,
-— .-_
A,
——
.——
7 h.
\
——
——
——
,,,
EX
PE
CT
ED
TE
ST
OI!I
RA
IVO
N(I
NM
uLT
IPLE
SO
FLO
WE
F4
TE
ST
MT
BF
)
-1
,,,–.
._,
‘,-
%!IL-!ID8K-7S?
OC CURVE
a=
p=
d=
10 percent20 percenX3.0:1
OG :.50 3.00 4.50 6.00 7.50 9.00
TRuE MTEF [xPRZSS[D As WuLTlpL~ OF ‘o, ‘+
FIG URE30 Tesl Plan XV1-O (Cont#nued)
225
MIL-HDBK-7B?
.. Slandord 7$ntd-durOl,O!, teSI Qlm4.4C ,.
. /’:___
4 23
i4 co
+
i/’
Sto.dard ficed-dwation k.! plan300 with ●orly rejection
3,60 + /
i340
~,:~ i
300 i
Z,no#
2 60i
2.40
42.20
2.CKI1
{
‘“0$ /,.60
1.40il
1.20
1.00
.80/1
.,G $ /
.~ o \/
~.20
0.00000 100 200 300 ● 00 5.00 600 700 e 00 9.0?
TRuE MTSF (IN MULTIPLES OF LoWER TEST MTBF )
PROGRAM MANAGER’S ASSESSMENT
FIGuRE 31, lest Plan XVII.0,
226
MIL-HDBK-781
OC CURVE
I
-.. -
flGURE31. Tesl Plan XVll-D. (Cont,nued)
227
20 percent20 percent
3.0:1
—
ExP
EC
TE
DT
ES
TD
UR
AT
ION
(IN
MIJ
LIIP
1.E
SO
FL.
OW
ER
TE
Sr
MT
8F)
,,,!,,
,,,,,,
,,,,,
,,
,.
——
.—
—.—
,t
—(,.
E
——
.——
.
—.
.L
—.—
.-—
——
Y
L
.)c.
.—c:
.!
1 ., ‘4!
i
.>..
_-—
-——
.>..
i,;
&.k
A“
33NU
ld331i40
AIII
IWU
OM
MIL-HDBK-781
.eo hi.60
.40
Y
plan
0.00 !.00 2.00 3.00 4.06 5.s9 6
TRuE MTBF (lN MuLTIPLES OF LOWER TEST MTeF)
I
FIGURE 33 Test Plan XXO
MIL-HDBK-781
UC CURVE
or 1.00 2.00 3.00 4.00 5.00 6.00TRUE H7BF [W’RISSCO AS MULTIPLE 0: 0., 91
‘aC
Q1
FiGuh I 33 lest Ran xX. E (Con[!nueci)
ExPE
CTE
DTE
STD
URA
TIC
IN{
INM
ULT
IPL4
SO
FLO
WER
TEST
MTB
FI
w
! —.
——
——
-.7-
–.,,
—,,,
..
.
.
UC imvE
1.00
c/.80 /
8 /sz: .60z
.00
.75 1.50 2.25 S.GG 1.75 4.5:.WL3
iiiii~ xiBF EXPP.[ . . . . - . .. . . . . . ...,. ,< UI, ITIDI r OF @o, @i
. 3,-! -a...=nt.)” p.! -.
= 30 percent
= 3.0:1
@o
%
FIGURE 34 Tesl Plan XXI. D. (Contlnuedl
233
. . . . . .
MIL-HDBK-781
REJECT /
I
I 20 --——- .- –
5
0
-— .
Cinargeabie
failures
ot234
s67a
RUEU
..—.
——
/
/
/
t, - U.721-2.W
/
L
/
/
/-
,_/f /I
ACCEPT \AND
coNTiNuETEST L/
+
4CCEPT
t, =0,72T .3.17
1s 20 25
TEST TIME ( IN MULTIPLES OF LOWER TEST MTBF, 6’l)Y
S:anda:c!ize{
Reject line
NIA
WANIA
.702.083.486.866.2’i
31:irnc.t?
Boundary line
4.40
5.797.1$
8.569.94
11.3412,72;d, io
1S.49
I
—chillgulb:e
failures
9101!
121314
15;6
DLIND.ARvLINE
/’/
#
5t2edarc!ized test !ime, t ?’
Reject line Boundary line
9.02I
16.8B
i 0.40 i8.261!.7? 1?.6513.18 21.0414.56 22.4215.95 23.8117.33 2s.19
1s.72 26.S8
1 Todelerrnine lh? actual tesl urn?. mult,.dy lie ~tand,wdfized te!l time [!.) by the l&er te$l MTBF I (7 )(See4 B.3 3 )
ALL-EQUIPMENT PRODUCTlON RELIABILITY ACCEPTANCE TEST PLAN.
FIGURE 3S Test Plan XVIII-D
234
I
.
PRO
BABI
LITY
OF
ACCE
PTAN
CE
“.
“r,
“m
m...
mk
“arr D
PRO
BABI
Ll”r
YO
FAC
CEPT
ANCE
T \ \ \ 1
..,,
.,,,
,,,,,,
,,.,,
,.,,,.
,.,,,,
,,,
,,,,
”
MJL-HDBK-781
ACCEPT AND
/
CONTINUE TLST REGION
\
REJECT REGION
i3
sINGLE FAILURS
BEYOND THE
B~Uf:DARY L!NE P.~L!C’~
~
1
ITOTAL 1[S1 TIME (IN MULTIPLES OF LOUER TEST MTBF #l!
NOTE : THIS IS NOT TEST PLAX VI II-D
FIGURE 36. Boundaw line criterion for reiect-acccDt decision
2361237
I
MIL.liDBK-7&l
~, ,otaI ,e$t ,,me is the ~Umrnation Of operating time of all units included in test *mP1e,,11 ,.,*h- ,=nda?d,zed te$t, ume(t) bythelower te$t MTBF(@t)1; TO dewmwne the aclua! :c25: Ome, m- .12., . . 5.-
(5WA833)
FIGURE 37. A1l.eQuipment test plan derived from Te$t Plan I-D
238
. ...>... -.. ..k_ ~=
MIL-HDBK-781
I
TRUE HTBF AS MULTIPLES OF 91
MII.-HDBK.781
I
I
I
!-—~—
CW<<,a”” R,, h% a = p = ,0 Pete., Rfl Icl ,Z BOUNDARY / /
O,%cmnm.l#o. R#!JfJ(.1! 1.5 1 UN1 , lIN[ /—.. —
REIEC7
Tf S1
/+’ /
7r
— .-5 10 15 20 2s 30
ChargeableI failures+.. .
0
11 2
I 3A
567
89
TOTAL TEST TIME (IN MULTIPLES OF LOWER TEST MT9F, 8 \ )IJ
Standardize
Reiect line
N/AN/ANIAN!A
0.70s1.92
3.144.355,57679
:st time. t 1
Boundary line
4.16
5.386.597.1319.02
10.2411.4612.6713.891s.10
Chargeablefailures
~o111213141516t71819
Standardized
Reject line
8.009.22
10.4311.6512.8714.081s.2916. s I17.7318.95
est time. t ~
Boundary line
16,32
17.5C
18.7519.97
21.18
22.40
23.6224.84
26.0527.26
Accept. reiecl criteria
~? TOtal te$t time i%the $Ummat,c,” O{ Ope,ating lime of all U“IIS included in lest sample.
~; To determine the actual [est tome. multiply the standardized test time (1) by the lower test MTBF (8:)
(See 4.8.3.3.)
FIGLJRE 38. A1l-eqwpment te~t plan derived from Tejl Plan H.D
240
n c-l
c ;0 m
0‘L
L
PRO
BABI
LI~Y
OF
ACCE
PTAN
CE.+
r . . . .
..
I
_
I I— —
n c a < m
I
MI1-HDBK-781
.
,,,,,,,0,, R,,i , a .8 . 10 Perct.1/
RClrC1 z
20
15
s
~.—1 Chargeable
failures
01
2
34
5678
TOTAL Tcslrwt (INMULIIPLt50r LOwtn TE5TM70f.@, 1$1
Standardize
Reject line—
NIA
N/A
N/A
N/A
1.15
2.5363.9225.308
6.69
w7.166 I 11
6.55 !2
9.938 !3
11.32A la
12.71 1514.096 }615.48
Standardized test time, t:
Reject line
8.089.47
10.8512.2413.6315.0116.3917.78
Boundary line
16.06
18.2519.6421.0312.4023.79
25.18
26.57
Accem-rejecl criteria
,. ?Olal [es! tiW islh.?%umma!.fiwof cwerattnqtimenl all vnit.$induded in test sample.j TOde,e, m,ne ,heac, ual tc$t ,,,ne, rn”ll, ply the,tandardtzed test tame (t) bylhelower leSt MTBF (0, )
(See A833)
FIGURE 39 A1l.eouioment test olanderived from Test Plan 111.D
242
1----------.-
I.
: w
-“ 6 c ,%
c“-
1-
— -. \ — . c % % — — —.
—
,.7 1’ 1,—
——— — \ —
.-?
1 \ t i i \ .
-r-
-— -—
,,,-.
-,-,
,,–
,–,,
,,,,,,
.
,, ~,
,, ,,
.——
——
—
0+.
——
.—
....
——
.—
——
—-
,.
——
.—
__—
—
\i
\l
q—.
:m r
\5 Y———
\
,,,,,,
,,,,,,
,,
——
—
——
—. . L : . L-—.- —
—:m
=[2
$:
.4
\\
\
-.
:
1.
OC CURVE
.0111~
1
.9 ~/
.6 Q\
,7 ~ 4
.61/
.3
.2i
.1
~.25 .5 .75 1.0 1.5 2.0 2.5 3.0
TRUE MTBF AS MULTIPLEs oF ‘1
FIGuRE 40. A1l-ecuipme!7! {es! glan d?~~v? d from Tesl Plan IV-D. (Continued)
245
i
IG ——-—
t
. . —
RHECT
,- I,6Aw-3.2V6
/
L
/
/
3
-z//ACCEPT
.+,2
TOTAL TEST TIME (IN MULTIPLES OF LOWER TEST MTBF 01)!’
I ~~,argea~!c Standardized leSt time. t ?’
failures Rejecl line Boundary line
iJ WAI
II 3.3C
WA. 494
;
I
o 6.59
3 I .65 e.24
4 3.30 9074.94 11.s4
l:!6.59 13. i6g.~fi !4.93
accept-reject cnterta
./
//
,/BOUNDARY
LINE
5
(jee4833i
1
f-r- mlmrr- .-., . . . .
TRUE t4TBF AS MULTIPLES OF ‘+
FIGuRE 41. Ail. ectu,pmentt.?%t Dlander, ved from lest Plan V-D. (C.anunued)
247
~lL. HDfj K-7Bl
0,<,,0. R4,L, a . /3 - 20Per’eu,t REJEC1 z BOUNOARY
0s,<r8rn#.a,tOnRalm (d! 30 1 LiiuE Z’ LINE
‘< ‘ / .~ “
3~7R.EcT ~--~”1,= 1.M8F -2.079
z
t
I
t
;2—
aACCEPT
.
/
ANDCONTINUE
ITEST
~’k
ACCEPT
,b ./1”0’9 II
1mAccepl-re)ecl Crlterla
!( TOIal te~, ,imel, lhe~ummal, On Of Opera~ing lime of all unils included inlesl%amp!e.
ZI TOde,erm, ne,heaclual,es, time, muli, plylheslandardized tesllime (l) bylhelower 1e%1MTBF( 81)
(See 6.63 3.j
a UJRVE
1 .0
.9
.8
MIL-HD&ii-i8i
I
fKfECT , ‘ BOUNDARY,
~.llzi
7
-I%+ .7+=
* ~
/
TOTAL TEST TIME (IN MULTIPLES OF LOWER TEST MTBF, “,]~’
I 6
N/AN/Al,lob~.j~
3.544.7s
~,$e I
3.764.97 I6.197.AO 18.62 IY.E.4
Accepl-re)ect Crllerla
A,II.eQ,, ipmPnt I.est plan derived from Test plan V1l-o
250
MIL-HDBK-581
cc a!?w
1
I
“:...5
.4
!.3 I I r
!.2 I i /IWlj /
I,,, ,,, . . .
,1 I ! l!
t- /f/~J/y I(-II 1 , I ,
.25 .5 .75 1. 1.25 1.50 2. 2.5 3.
TRUE MTBF AS MULTIPLES OF e]
FIGURE 43 A1l-eau,gmentte%t plan derived from Test Plan VII-G (Cmmnuedl
251
CH
AR
Gr
AB
LEF
AIL
UR
ES
I
—.
L.JK
I-.
O
——
N,-
::z
&:s
:
—.
y!,b
y,-
aw.g
~
——
,
0..
.-.._
.,_
__ !
I t
-’__
____
3 -1 D ,- Zh -t “\N—
-—
——
z m :ic
e
\
.,,.
,.,,
,,,,,,
,,,,.,
,.,,,
L,.25 .5 .75 1.0 l.< 2.0 .?.5 3.0
TRUE MTBF AS MULTIPLES OF 91
MIL-HDBK-781
I
----- --- ;
----- --- ;
x III----- ----I
----- --- x
----- --- ;
1 I:I
ltl FAILURE T*LI Znd FAILIJRE TIME
FIGURE 45
,.. - -- .:--- .-..—. . .- —.- . . . . .._
Time truncation (tvve I censoring]
254
. . . . . .. .. ..-. ._ ._. <r4.s _. ~+...__ ._ -_..-.. —... .
MI!.-HDBK-7EJ1
---
\-------
I
0.) 3wllVl13dw31
255
—
MIL-HDBK-781
I
V18RATION.25PC12CEN1RANDOMPREStLfCIEO DUTYCVCLt
/
uAl;t
COLD i:SOAK ,. :
(s:.701[s :2.3. a”d~) ,; LOW TEMPERATURE
HOTSOAX
!@N5?HcYcLtl
1 1
lfME-MOURS
NOTES:
1, Rate OYchamber temperature chan?e shall be a minimum of 5°C per minute. unle>~ Othe~i$especif, ed or approved by the procurtng activily.
2 Moisture level 10 be sufficient to cause vi~ible condensation, frosting, and freezing
3 Hot soak and cold soak are optional
A. V, Lwaloon, electrical stress, duty cycle OFF
F;GLI,Q: 47, Co-,5, ned e,n.v:ronmec:a! te; : prcf:le !07 mcbile Crcwnd e~uicmenl
256
1
?w::L-HD3K-7E?
I .
I
-:
HIGH OFF
,,,., ~NOMINAL
.- 4--I
LOW ; 1 VOLTAGE
I
I
/
/
/
/
/
/
/
~~’’””COLD ,-35
SOAK 2 4 6 8 10 12 14 16 18 20 22 24
TIME (HOURS)
t-
-So.c
FIGURE 48. Naval surface crab mission environmental profile for ex.lernallv mounled eQutPmenl ( cOld cvcle}
257
MIL-HDBK-781
45
35
3a
25
2[
_. — .
HIGH I I
1 I 1I
INPU T NOMINAL I
VOLTAGE II
DUTY CVCLE LOWI I
)N I J
}FFI1 II
VIBRATEON - 25% RANOOM PRESELE~O OUTV CVCLE1
60”CHOT SOAK
r
‘1)
FIGuRE 49. Naval surface craft mission environmental profile for eflemallv mounledeauiDment (hot WClel.
I I , I , I t I , 1 I
10 20 30 40 so 60
‘TIME IHOURS)
258
MIL-HDBK-781
I
HIGHt
INPUT iNOWiNAL
iVOLTAGE I
ION: OUW CVCLE
L!OFF :
I VIBRATION - 25% RANOOM PRESELE~EO DUTV CYCLE
,,
,16
F’
12
10
8
It
IttCOL[SOAI
‘L-w.{
I
I I I I I I I I I Iz 4 6 8 10 12 14 16 10 20 22
TIME (HOURS)
FIGURE 50. Naval surface craft miswon environmental Prof)le for internally mounted eaU!Dment ( cOld cvcle ~- 1
259
MIL-HDBK-781
.—i- ‘“
,1
HIGH 1 1 I
55
50
45
3s
30
25
20
IN 1 i NOMINALt1
—. PuTLOW VOLTAGE
I1-
ml DLflV CVCLE i
OFFL
VIBRAllON - 25% RANDOM PRESELE~ED DUTY CVCLE
65XHOT SOAK
I I I , I , I , I !
10 20 30 40 50 60 70
TfME (HOURS)
FIGURE S1. Nawal surface craft mission environmental orofik (or internally mounted eaui Dment (hot cvcle ).
260
I
5C
45
4[
1’
,
(
IHIGH I
1 1 WXAi%&La-l- NPUT
)W: J VOLTAGE J4
)N i OUW CVCLE
FF :
VIBRATION - 25Y* RANDOM PRESELE~EO DUTV CVCLE
I I I I I , I I I I I I
4 6 B 10 12 16 i6 i~ RI 22 :G
TIME (HOURS)
-E&c
FIG UR.E 52. Naval surface crafi. mission environmental PrOfile ‘Or internally mOun:ed
eaui Dment ( temperature controlled 1.
261
MIL-HDBK-7S1
HIGH II
INPUT I I NOMINAL I I1 I
LOWI
VOLTAGE Ii }
ON DUW CVCLE II
OFF
I I
vmRAnoN -25*A RANDOM PREsELEmD ouTv CVCLE
II 1I ~5.c I
t HOT IISOAK I
S5
50
45
40
35
30
25
20
15
10 -
s
o
-5 I ! I ( I I , [ I t I I I I { ,
140 142 144 146 148 1so 152 154 156 158 160 162 164 166 1
TEST 71ME (HOURS)
8
FIGURE 53 Naval wr(ace craft, mission environmental profile for internally moumed eguipmen[
jtemperature controlled).
262
.010
,009
.008
.(10
7;
C106
< ..rJ1
35-M ~
,004
lx P :.0
03& WI ‘x .
.002
g n.
.001
——
==
= /’——
.—
——
.
—.
1020
— —-
——
——
— —-
— —-
FREQ
UENC
YHz
vibr
atio
nsc
hwfu
le:
3ho
urs
out
Of
a?L
-hou
rc~
l~.—
.—
.-—
——
——
App
lysp
.rlru
mA
once
for
10m
in.
(5m
in.
up/5
min
.d$
wn)
10m
lnut
e~w
ithW
)~
[l~r;
at’1
7n
AIIO
IV<
prct
rum
B[O
r20
min
.(I
I:,”,
)w
ith1’
3-%
Hw
4JIm
cvH
rnt
i’i~
,,,~
ci>
rr:h
kshr
t~”e
pnC
YC
ICS
h.R
attle
d.’fn
aqe
spec
trum
B.
lr~,n
spor
tatio
rra
ndom
spec
trum
.-.
—.—
...
..
.——
--—
FIG
UR
ES
4~
wfa
cecr
aft
and
$ubm
atin
e~
rtix
??Q
w2
,,,,,,
,-—
...=
.,,,
,.,,,.
—.
—.,
{1,—
00
:--
---
--=
----
----
--%
----
--‘
7
‘)
I.,,
,.,,
.,,,.,
.,.,
.,,,.
,,.,
,,..,,
.,,,.,
,,,,,,.
.,,,,,
,,,,
,,,
,,,,,,
,,.
I
--- !.””
.—
aPProved by the Procuring acuvlty. -MOIit”re I=iel:0 be wff!c,en. , la cause visible condensation. frosting, and freezingHot soak and cold soak are opuonalVibration, electrical stress, duty cycle OFF.
NOTES:1. Rate of chamber temperature change $hall be a minimum of SOC per mmute. unless otherwise specified or
2.?4.
FIGURE 56 combined enwronmenlai Iesl Profiie iul m~rir,e trd$. KiUiP-.en~
265
,.-
‘~T I i
I I 1}
I
Il\l\
I II Ill IvIv \ .-
lTME (MINUTES)
Mi>sion Type
LOW-LOW-LOW
Ferry
Seek & Attack
Surface surveillance
Ferry
Ferry
Characteri$:icsI II
AITACK AIRCRAFT
Allitude [1000 h)~- ~
2Mach No. (M) 0.6 O.aDcrat!e.n (mum ! 2 60
Alt#tude ( 1000 h) &J~
Mach No. (M) O.bDurat;on (m(n) 10
ANTISUBMARINE WARFARF. AIRCRAFT
Allilude (1000 h) o-do 40
Mach No.(M) 0.6 0.6Zura[iurt {mnr,.; 15 ~~
Altitude ( 1000 h) 0.1Mach No. (M) 0.6Dural,on (min.) 5
Altiiude (10!20 S.) f).~e
Mach No. !M! 0.6Duration (mIn.) 14
Ps,ii;e
Ill
20.68
8
32i3.6si
28s
4U0.65265
1
0.25448
380.6565
ELECTRONIC COUNTERMEASURES zNRCWFT
A!:itwde (!000 ft) n.1’j 35Mach No. (M) 0.6 0.7Ourat,on (mtn.) 13 242
Iv
~
0.467
40
0.655
v
~~
0.43
32.LI
0.410
40.00.420
\ .0
0.47
38.00.4
2\
35-o0.420
266
MIL-HDBK-781
I
I
Mi$sion Type
LOW-LOW-LOW
Ferry
LOW. LOW. LOW
Ferry
LOW-LOW-LOWreluel Ong
Strike refuel
CharacteristicsI (1
FIGHTER AIRCRAFT
Altitude (1000 ft) 0-1 1Mach No. (M) 0.7 0.5Duralion [min.) 2 68
Alotude (1000 ft) o-35Mach No. (M) 0.7Durat!on (mtn.) 12
RECONNAISSANCE AIRCRAFT
AlliIude ( 1000 ft) 0.1Mach No. (M) 0.7 0:9Duration (m, n.) 2 63
Altitude (1000 ft) 0-38Mach No. (M) 0.7Ouration (min.) 13
TANKER AIRCRAFT
Altitude (1000h) o-5 5Mach No. (M) 0.6 0.44
Duration (mIn.) 4 40
Alutude (1000 ft) 0-15 15Mach No. (M) 0.6 0.58
PhaseIll
1
0.75
350.7231
0;910
380.74
244
5
0.4460
15
0.47Duratmn (min.) 0.7 24 58
Iv
1
0.s72
1
0.49
67
5
0.4437
150.5E
19
v
1-0
0.5
3
35.00.517
1-0
0.5
3
38.0
0.518
5-o
0.46
15.0
0.411
I
FIGURE 57. General mistion pro foleand charafleristics forsixaircrati tvvesand twelve missions (Continued)
MIL-tiDBK-781
Mv,,,t
h%!,Mv,,
W W Mv, VII
Illi
h .
II Iv v VI WI
M,x
\(
—.
llME (MINIJTES)
Mis., cm TyDe
Close%upport
High. Low. High
In.esugat, on
anti Atlack
ContactInvestigation
Characteri$W\I
Phase
1! Ill Iv v
ATTACK AtliCRAFT
32 32.5 5 50.6E 040 0,73 0.83762 ~ 61 7
32 32-1 1 NIA
0.6: 0.L?5 0.84 NIA
55 u 5 WA
VI VI! Vlll lx
AIIiIude (1000 h) 0.32Mach No.(M) 0.607Ouration (m~n.) 5
Altitude (1OOOW o-32Mach No. (M) 0.60Duration (min.) 5
WANIANIA
5-400.70
6
40
0.6863
AO
0.6851
40.00.4C
17
40.0
0.4018
NIA
WANIA
1-40
0.705
ANTI-SUBMARINE AIRCMFT
Altilude (1000 fl) 0-38 38 38.0.5 0.S N/A
Mach No. (M) 0.6 0.6 O.A 0.25 NIA
Duration (min.) 6 155 9 120 NIA
Allitude ( 1000 ft) 0.20 20 20.1 1 NIA
NIANIANIA
0.5-400.75
40
0.6140
40
0.6108
40
0.7127
40.00,4
10
NIA
NIAWA
1-40
0.75
40-0
0.410
Mach No. (M) 0.6 0.7 0.4 04 NIA
and Intermediate Duration (min.) 4 .s6 6 211 NIA
Altitude ( 1000 ft) 0.36 36 36.1 1 NIA
Mine Mach No.(M) 0.6 0.6 0.4 0.6 N/A
Lay, ng Durat,on {min.) 6 140 9 20 WA
WAN/ANIA
1-40
0.7s
40.0
0.48
FIGURE 58 General mission Drofile and characwri$lics for six ailcraft lvDes and twelve miss, ons
268
I
MIL-HDBK-781
. . ..- . . .. . .. . -.tmaranemucs rnaseI II Ill Iv v VI
ELECfRONIC COUNTERMEASURES AIRCRA~
w Vlll lx
36-O0.40
12
35.00.40
16
40-0
0.517
42-o
0.519
40.0
0.s17
40.0
0.517
40.0
0.418
34 34.1 1Altitude (1000ft) &34Mach No. (M] 0.6Durallon(m, n.) 10
Altnude[1000fl) O-33
Mach No. (M) 0.60Duration (m,n.) 10
10..90
5
NIA
NIANIA
1
0.5029
1.36
0.708
360.58
29
Penetration
Standoff
0.s7 0.85 0.s032 5 29
33 33.30 30
0.70 0.60 0.6742 1 49
FIGHTER AIRCRAFT
35 3s-10 10
0.7 0.9 1.0
87 3 7
30 30-1 1
0.7 0,85 0.857 5 11
30 3-5 50.7 0.8s 0.4269 3 59
30.35
0.701
NIA
NIANIA
35
0.7041
Altitude (1000fI) 0.35Mach No. (M) 0.7Duralton (min.) 8
Allilude(1000fl) 0.30
Mach No. (M) 0.7D“rat,an (min.) 7
Alt,lude(1000fl) 0.30
Mach No. (M) 0.7Durauon (m,n.) 7
N/ANIAN/A
1
0.857
NIANIA
NIA
N/A
N/ANIA
10.40
0.87
40
0.775
Escofl
42
0.766
Htgh-LowLow-ti,gh
1
0.85
9
1-42
0.856
Close
SuppofiNIA
NIANIA
5-400.85
A
40
0.774
RECONNAISSANCE AIRCWFT
High-Low.H,gh
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FIGuRE 58
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269
MIL-HDBK-781
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Altitude (1000 h) 0-38 38 NIA NIAHigh-High-High Mach No.(M) 0.6 0.6 NIA NIA
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FIGHTER AIRCRAFT
Altitude (1000 fl) O-35 35 35 NIAHigh-High-High Mach No. (M) 0.7 0.7 0.9 NIA
Duration (min.) 7 46 5 NIA
Allft”de (1000 R) O-35 3s 3s 3sAir Defense/ Mach No. (M) 0.7 0.7 0.67 1.35Capture Durattion (min.) 7 16 60 4
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MIL.iiDBK-781
Mis!ion Type Characteristics PhawI II Ill IV v VI Vll
RECONNAISSANCE AIRCRAFT
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Low-Low-High Mach No. [M] 0.7 0.75 0.9 NIA 0.9 0.75 0.5Duration (min.) 1 52 10 NIA 7 60 13
Alt,tude [1000fI) 0.35 3s 35 NIA 35-40 40 40.0High-subsonic M,ach No. (M) 0.7 0.85 0.9 NIA 0.8S 0.5
Duration (mtn.) 7 58 16 WA 2 64 13
FIGURE 59. General mission prof,le and character+ st, cs for four aircraft typ es and seven mtswom (Conljnued)
271
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FIGURE 60 General mijjion Drofile and characteristics for an atlaCk aircraft on a hiGh-iCmw-lOw-F, i~h m,i$i,~fi
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TIME (MIN~S)
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CLIMBMach nuii - 0.75 CLIMB
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CRUISEAltitu~ooo ft
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317
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ugh
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——
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FIG
UR
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1 1
MIL-HC3EK.7E1
?3436799, 23 4 $879* I 234e67m9t,.2 *8
, , I 1, I 1 I 1
,.O
, n-
LINE EOUATIONS:
‘~~~1 , (~~~~o~) ,Qrms [oVL] : (IOL
[EXP] = [LOG, ofa)l - 12.2S5332)]
(FAcTOR);’- sEE TABLE 48
Q(MIN) S. Q ~ q(MAX)
332
MIL-HDEIK-781
I t
I
I I Hlllli
. . .
I Illllllly,{lllll]. ,/l,; f I II
,/
, ‘/,, .,,!l\ l,,,,
IO’ *L- zI 1 I I I 1 II I 1 1 , 4 , / A-,,, ,,, , .- ...,1 1 1 1 1 , I
I ! I I I t-t
I I I 11111 II I I 1 H
-1-u
LINE EOUATIONS:
~rm, ~ovL) , ,,0 [ExF]) (FACTOR), (FACTOR)i --sEE TAE)LE 4s
[EXP] = [LOGto(Qli - (2.285332)1 qlMIN) S. Q < a (MAx)
NOTE: THIS FIGURE uSEO IN CONJUNCTION WITH TABLE 46
333
MIL-HDBK-781
~u,v,, IttuOPE
49/ OCTAVE
M
,
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10*,c?b
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.
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IMINIMuM OVERALL Qrm%
5,I
,. F9P. ebc!+ NO. c (2.45 l~ii~l.!,1 !.I
I I1
i
I r I 1 I I I II I 1 I ! 1 , 1 1!
.L— ~ ((MINI S. (sEE TABLE 48) I
s I I
I
t-
1 II
1 I I!,!,
2 1
I II a, OYNAMIC PRESSURE 1. 1[ ‘1(l b/ft2)
,~-1 I
LINE EOUATIONS :
arms IOVL) , (10 [EXPJ ) (FACTOR I, {FACTOR) i ‘- sEE TABLE 4E
[ExP~ : [LOG;C(a): - 12.2a5332~ tl(MIN) S a S q lMAx)
NOTE: TMIS FIGuRE uSEO IN CONJUNCTION WITH TA9LE 48.
FIGuRE 13A, Random vibration max!mum pred, cted environment for air.to-air (AAM) a,r.launched
w~$
334
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MIL-HDBK-781
.
(a) MING AND FIN-TIP LOCATIONS ONLY ON A~
r
N
g,rn,(WL) =E
& ● 1.3 (CONSTANT) fi~c~(grnJ(See TABLE 48 )
i-lft=SHz
W. -(1 .69) Xo (5EE TABLE 49) (See NOTE)
Wo .-7 f~=2000Hz
z I0 y I
-ada PtRoclavE20sf25100Hz
r< w- 1R -m k, I
;i1 %1
<f2 = 3rd rigid body wing-
1 pylon-store frequency
1(Hz). otherwi~e,
f,f2 (rein)- 20 liz,Hz. fZ
*2 1. (ma.)= 100 Hz. ral QuEMcv (Ml)
USCwIT1’1fOUIPMINT RtOuIRttii N15 FROMFIGunEt36b Swl LLASWITH fULLV A5S1MBLCDlX1t FINfiLSTORE.
(b) ALL PVLON LOCATIONS ON AIRCRAFT
vN
g,m, (OW -~
A; = 1.3 (CONSTANT)
i-l
(SEE FIGuRES 132 THROUGH 134)
Wo3dB PER OCF&V1
I ~,I
1 1~,
I I
I I
I It
1, *2 b
FREOUENCV(Hz)
f, w 20 Hz
f2 - (Calculated from f3and Wovalues)
f3 = (Calculate according to table514.3-VI, Method 514.3, MIL.STD-81OD.
f. -2000 Hz (if f3z 1200 Hz,otherwise. f~ofl . 100 Hz)
w~ = Igrm, [OVL)12R0
Wt ● [9rm\(OVL)12 RI
(See TABLE 49)
NOTE:USE FOR ALL OVNAMIC PRESSURES(q) AT ALL LOCATIONS. EXCEPT AS UMITEO 9V (a) ABOVE.MINIMUM g,~, (OVL)=l.3 (SEE TABLE 48) [
FIGuRE 13S. Assembled eaternal stores andair-launched weaPons-vi brati0nalresoonse
acceleration PSD versus freauency soectra.
335
MIL-HDBK-781
r N
arm, (OVL) = ~ A,
i-l
(SEE Fi13uREs 132 THROUGH 134)
MB ●EM O~AVf7 I
YIIII
I d, AII
; I
I I
I I I
I I
t, f> t,
FRIQutMCV (H,)
fl m20 Hz
fz _ (Calculate from f3 and W. values)
f3 _ (Calculate according to TABLE 514.3-vI.Method 514.3, MIL-STD.81O)
f,-fJ* wOoHz[sf~)
f~ .2000 Hz
WO = [grm, (OVL)]~ ~.
W, _ [grm, (OVL)]? ~,
(SEE TABLE 49)
/- -MB ●a ocrAvL
NOTE:USe in conjunction with”the limits shown in FIGURE 13 S(a). For qsq (rein) (see TABLE 48) and MachsO.4S, mimmum g,m, (OVL). 1.3
FIGURE 136. Equipment installed in a$sembled external stores and air-launched weapon$-vibrational
I remonse acceleration PSD versus freauencv spectra.
336
2.0
1.0
0.1
0.01
fq=5Hz
f2 - Fiwt rigid body wing-pylon-store frequency [Hz)mherwise. f t Sfz ~ fl
f, .20 Hz
1!
I
1
f, f~ f~
FREQUENCY (tiZ)
Test duration = 6(X) seconds (minimum totalt:~~refr each mission profile = 18 seconds
x- f4umber of buffet maneuvers (minimum of 3,phased durin mission rofila). Maneuver
“i” 4“conditions In uon bu et Include (but arenotl!m!tedtol:tif}-g diveanack.tight twnsRPO, and high an low speed: tails.
6- Avarage induced buffet duration, in seconds.
NOTES: 11. This spectrum will be superimposed on the applicable acceleration PSD spectra Of FIGURES 135 \
and 136, according to the mission profile definition of flight phasing. I2. Weight reduct!on factor not applicable for th!s spectrum.3. See TABLE 49 for Equations to solve for Ml, M2, AI and Al.
FIGuRE 137. Induced b“ffe! maneuver random vibrat, on response spectrum
337
- . —e.. —--
ALT
ITuD
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T.
uz
z
180
SE
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&h%m9-’J.1w?4+zh-$IGURE 139 Environmental engineer; na rxoqram schematic
339
m, ,,,. ,s =,, !-, _= , ._.,...,- .-.., e....- —.-
——
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1. ASSUMED CAPTIVE
FLIGHTAAUNCM
R1lRflVAL
2. ●ERIODIC
MAINIENAMCE
lN5Pf CTION
CALINDAR
3. uWCMEDULf D
MAIN1tN*WCt
(lSTIMATCO)
4. 0i5. KS:%t=LYl
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,
FIGURE 141.
5 VfARrOTALS
(15)
(5)
(20)
(s)
(7)
36 a 60
Eurooean scenario assumed maintenance schedule and Dossible operat, onar
uttltzauon rate for envlrOnmenlal analvm (example).
341
—
..
.,
.,.
.
—-
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—.-—
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FIGURE Estimated percentage of ttme d,str, bufion for tranwmnation. holdldelav. and handltno.
for nom, nal-orobable factorv-to-theate, movement ttmeline
344
.-
——
.a
.—
ouiu
wuadm
31
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MIL-!iDBK-781
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1 346
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Mubl
clcl
l
MIL-HCM!G78?
{HIGH-LOW-HIGH)
STANCM,RU DAY
,. “,”32. SEC
2 U?”s. . . .
50
t
2 ■lus. . s..
:0s!”s23 Sec.
24-C
I, . . .
\J z ●,.S
I37 SEC,
\
L=ExJ20 M1.sIf, :::,
“.0 6,s,4 ❑INS30 Sf-c
~ ‘7’0” ‘ ‘
4“, ”s12SEC
\
l,” C - “,”9,
FIGuRE 145 Assumed twxcal altack a,rcrafl operatina enveiope (standard oavi showina the assumeci h,qt>-
1Iow-h, Qh m,ss[on pro f,ie. (Conl, rweci)
I
348
MiL-HCt6K-761
I
I
I
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m
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For
max
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tmdu
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FIG
UR
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for
th?
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.(95
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IGU
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149
at3
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tack
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tspe
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with
50.p
erce
ntfo
r6
seco
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emh.
conf
iden
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wd
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one-
side
d22
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limit)
.
11.2
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INS
–—
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WE
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figur
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IGU
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144,
and
TA
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52m
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bead
just
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the
fact
orin
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!Bto
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53
(thi
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144
exce
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rw!
min
imum
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llz{e
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ree
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UR
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ile(I
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we
with
FIG
UR
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131
thru
t34
and
TA
BLE
48_—
——
——
——
GIe
)—
—
1flo
SEC
S
—
I I
w m N
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----
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Wll L-HDBK-781
i
I I
C. ON-BOARD ECW!WMENT H!f3H SPEED
SeeFIGURE 135 (A) for wing and, fin tip installation. Wt rffsq -~t lg,~, (OVL))Z vibration factorothew.vse, s:e et e.!! dynsnvc pressures. q.
‘WO(TISTI - W, i9,m* @~Lj)2 wibraii~n fMOF
e (No weight reduction factor)~=: ; qz250 !LV f@.. P&.:.h =(!.45
& 5.E!$X!O-4
: ‘“
[
3d9!@~AYE ‘j,:~~ - 3db KFCTAVE
$I
w;
,\g~, (OVL) = 1.0
“1 I I
1g
!
<I 1 I
1 I I
20,W
Soo~m
iOOO
FREOUENCV @iZ)
1.0
0.1
Co?
Time of application of spectrum :6 seconds. perOCcwrk?roce, =Infrnufi, 3 O:<ur:en<e: per .=; ::18!?.
ft-SHz
f2 mFirst rioid body wing-pylon-store frequency (Hz)othew”ise, ft Sfz sf~
f~ .20 Hz
I
1
0.001
fl f~ :3
FREQUENCY (Hz)
~f!wEs;1. This spectrum will be superimposed on the applicable acceleration PSO spectra of FIGURES 13S I
and 136. according to the mission profile definition of flight phasing of buf+e~.
I ~ See TABLE 49 fo,eauationsto solve forR4,, MZ,A, andAz.‘.”.reigtik raiiuc; io,-l fa.fiw riot appliceb:e %: :%8 :p2ctwm ~
FIGuRE 149 U“il.gaM5 (OVL)-acceleration PSD versus frequency spectra (continued)
, -“-.
353
.
lfl -:
,,:.
IW<.%
Rc.10-4
1
10-5~, 1 , , , i , I I 1 , , I , I # , 1 ! t , II.”J 10 100 1000
FREQUENCY (Hz )
FIGuRE 150 Vibrat,on p!ofdes for rail !ransportatlon
354
1~13M
r191:l
(SWIN1il)3W11
0:s,
Ozc082
Obl
—-%
-JJ+--l--
001—
~—
-r-+%
10000“
.—
-—1
——
[000”0=
—--
——
——
{
G-
—..—
—100”
>N
J.-
10”-
———‘“sauurm
rA
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49.
..
MIL-H13BK-781
0020,
O030Coo40r
O05C0060
007000s0<Oo90c01 Ooc01100120 5000013001400150 50100330<
034003500360 505003700380 5060039004000410 507004200425cIM30
04400445 5040
04500460 100470C0480c0490C
0500<05toc
0520<05300540
0550
Appro, imatefy optimum Rel, abrlity bounds
read m3, v3, m2. v2, m 1, vI, sf201, c(20), tm, 2(20),22(20). z3(20),
8 z4(20), tk, suml. wm2, sum3, sum4, wm5, rinteger k, nf(20), n,l
Input # \ystems, time on ten, # failures
print 5000format (2x, ‘Give number of subsywem~.-)
read (5,6060)kprint 5010
format (2x, - Enter data \tarting by subsy!tem with !mallest total time on test. -)
dol Oi=l,kprint 5050,1
formal(2x, ‘Enter data for $ubsystem’’,ti4)print 5060
format (2x.-Enter this subsystem’s total timeon lest. -)read (5,6060) z(i)prOnt 5070
format (2,, -En!er th,s subsystem’s numbm of failures. -)read( 5.6060) nf(, )
if (nf(i) .gt O) go to 10prim 5040
format (2a, ”’Zero failures: analysis impossible “)
go to 105continue
Second pan:
Calculation of M and V
Preliminaries:
Do ZOi= l.kzl(i] = l. Ofz(i)
z2(i) = 1.Ol(z(i). z(i))
FIGURE 152. Proaram Iistina for FORTRAN Droaram,
356
MIL-HDBK-781
05600570
C&o 20
0590C0600cc0610cc
0620 5080
0630CC 3006m0650C0660c06700660
0690g?~o
0710C0720
07300740
075a
(
z3(i)= 1.0/( 20)””3)zd(ij = 1.O/z(i)” J
cor,tifiue
Do30i.l,k
print 5080, z(i),zl(i)t z2(i),z3(i). ~4(ilformat [2x.f 12.3,2x4(f 12.9,2x))continue
More than one faiIurelsubq.Tt@m
suml .0.0
wm2 = 0.0wm3 = 0.0
SW?!4 = 0.0
Do40i=l, k
n = nf(i)-1suml =wmi +in=zi(ii);tifi2 = n’z2(i) + ;urc2
FIGURE 152. Proaram Iistina for FORTRAN prcmram - Continued.
MIL-HDBK-78?
k)7tiG077C
0790 40
0795CC0800 50900860C0870COEaoc089009000910cc0920 6000
0930C0940{C950C
I 096009700972c<
I 0974 60050980r
I 0990<1000110IO1020103C1040 5010501060
10701080
1090
1100 601110
1120
I 125cc
wm3 = n“z3(i) + wmiwm4 = n.z4(I) + sumf
continue
print 5090,wm 1, wm2, sum3, wm4
format(4(f10.6,2 i))
Orig;nal paper ( I 972!
ml = suml * wm31sum2
v! . sum2 + sum4Aum2print 6000,m l,v1
formai(21,”Ml = ‘, f10.7.3x. -Vl =. f10.7)
Modified ver$ion (1974)
m2=suml +21(1)v2=wm2+z2 (l)prim 6005, m2. .2
format (2x, ‘M2= ‘, f10 7, 3x, ‘V2 = “,f10.7)
The Case of Only One Failure:
Tk=O.O
Do50i= I,ktk =tk + nf(, )
continuetk = tktfloat (k)
do60i= l,kn= nf(i)+ 1s(i) = (z(i) -z(l) )/(ik’. n)s(i) = z(i). s(i)
continue
do70i=l,kc(i) = nf(l). 1 + ((z(i)/(k”J(i)) )”.2)prim 601°,i, s(i), i, c(i)
FIGuRE 153. Proaram Iistinq for FORTRAN oroaram.
358
.,
MiL.1-iDBK-781
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1.
li3i2 73!14c! 6IJ1O11Soc
116011701160!1901zoo
121012201230
1260
125012601270
129o 801295CC
:308 S020131OC132o1330
1332cc
1334 60251340C1350C
ccmtimi2
formal (2r, ‘J[”,i3, -) = ‘. f10.5.2x. -c(”,i3,” = ‘, f10,5)
suml =0.0sum2 = 0.0wm2=0. O
5s!!!4 = C!,owm5. O.O
do80i=l,kn = nf(i).1
suml = w’s(i) + wm icwn2 = e.j(~i)”~i)) * SL,!?!~
sum3 = wcm3r(c(i)f(s(i) ”z(i)”z(i)))wm4 = wm4 + (c(i)l(($(i)””2 )”(z(i)””2)))
wmS = sum5 + (c(i)llz(i)””2))
continueprifii 6020, 5iJtil,Wfi2, $U=3, W~4, Zti-5
!ormat !2z,S(f 10.7.31))
m3=suml .wm3/wm5W3. wm2. wmusum5print 6i125, m3, v3
format [~z,-M3 = -,f IO.3,21.-V3 = ‘,flo 7)
Calculation of bounds
FIGURE 153. %w-rarn !istin~ for FORTRAN oroaram - Continued.
359
MIL-HDBK-781
1360(1370 50G1375
13801390 6030140014101420 6035
14301432143414351436 6032
1437143S 603614391436 6037!44C<
1445C14SOC14601465
:47014751480<1485C
1490C14951500 60401510
1520 60501510
1520 6050
1530153215401545 6060
1550 105
romnueprint 6037
print 6030format (2., ” Enter confidence Ie.e) percentile.-)
read (5.6060)p
pring 6035format (2x,-Enter mission time.-)
read [5.6060)imprint 6037print 6037print 6032. cm
formal (2 E,-Mission Time: -. f10.5)print 6036,P
format (6x.. Percentile:-, f10.5)print 6037
format (3X)
ca!l resu!t. {ml,vl,tm p,r)print 6000,m I,vlprim 6040, ~
call rewlt (m2. v2. tm, p,r)print 6005, m2, V2prini SOSO,rprfint 6037
call result (m3. v3,tm, p,r)prom 6025, m3,v3
print 6040,rprint 6037
formal (2x,-Reliability Bound ,$: ‘,f 10.6)print 6050
format (2... Reliability Bound is:., f 10.6)
print 6050
format (2x, ‘If another confidence level or mission time, give l.-)
read (5,6060) 1print 6037
if (1. eq.l)g0t0500format (v)
continue
FIGURE 1S4. Prwramlistina for FORTR4Noroaram.
360
,- ,>,
I
1s6015701590C
1s%)! 600161OC
162016301640!~~o
165516601670
stop
●nd
r = p“(sqdv])K3.O”m)r = 1.0-(v/(9.0”m” m)) + rr=r””?
r=tm”m”rr = exp(r)
return●nd
,
FIGuRE 15A. Prooram Iistina for FORTRAN woaram - Continued.
361/362
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