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A MANNING AND MAINTENANCE EFFECTIVENESSMODEL APPLIED TO THE COMMUNICATIONDIVISION OF A "KNOX" CLASS DESTROYER
ESCORT.
Clifford Stephen Perrin
NAVAL POSTGRADUATE SCHOOL
Monterey, California
THESIS• A MANNING AND MAINTENANCE EFFECTIVENESSMODEL APPLIED TO THE COMMUNICATION DIVISION
OF A "KNOX" CLASS DESTROYER ESCORT
by
Clifford Stephen Perrin
September 1975
Thesis Advisor: Donald P. Gaver
Approved for public release; distribution unlimited.
I 9
SECURITY CLASSIFICATION OF THIS PAGE (Whan Data Rnf.r.d)
REPORT DOCUMENTATION PAGE READ INSTRUCTIONSBEFORE COMPLETING FORM
1. REPORT NUMBER 2. GOVT ACCESSION NO 3. RECIPIENT'S CATALOG NUMBER
4. TITLE (and Subtltl*)
A MANNING AND MAINTENANCE EFFECTIVENESSMODE! APPLIED TO THE COMMUNICATIONDIVISION OF A "KNOX" CLASS DESTROYER
5. TYPE OF REPORT ft PERIOD COVERED
Master's ThesisSeptember 1975
• . PERFORMING ORG. REPORT NUMBER
§ AUTHORfa; • CONTRACT OR GRANT NUMBERS.)
Clifford Stephen Perrin
*. PERFORMING ORGANIZATION NAME AND ADDRESS
Naval Postgraduate SchoolMonterey, California 93940
10. PROGRAM ELEMENT. PROJECT, TASKAREA 4 WORK UNIT NUMBERS
11. CONTROLLING OFFICE NAME AND ADDRESS
Naval Postgraduate SchoolMonterey, California 93940
12. REPORT OATE
September 197513. NUMBER OF PAGES
5714. MONITORING AGENCY NAME & ADDRESSf// dlllarant from Controlling Olllca)
Naval Postgraduate SchoolMonterey, California 93940
IS. SECURITY CLASS, (ol thla report.)
Unclassified
15«. DECLASSIFI CATION/ DOWN GRADINGSCHEDULE
16. DISTRIBUTION ST AT EMEN T (ol thi • Rtport)
Approved for public release; distribution unlimited.
17. DISTRIBUTION STATEMENT (ol tha abatract antarad In Block 20, II dlllarant from Raport)
18. SUPPLEMENTARY NOTES
19. KEY WORDS (Contlnua on rararaa alda II nacaaaary and tdantlty by block numbar)
Reliability, Readiness, Maintenance, Balance Equations
20. ABSTRACT (Contlnua on ravaraa alda II nacaaaary and Idantlty by block numbar)
The studyship manningand repair ardata analytictenance and MData Collectirates, repair
objective was to investigate the problems ofeffectiveness, specifically in the maintenanceeas, using various probabilistic modeling andal techniques of operations research. Main-aterial Management data from the Maintenanceon System were used for estimating failurerates and maintenance deferral rates for each
DD t*j
(Page 1)
F
aT71 1473 EDITION OF 1 NOV 65 IS OBSOLETES/N 0102-014- 660 1 |
SECURITY CLASSIFICATION OF THIS PAGE (Wnan Data Kntarad)
ffliCUWlTV CLASSIFICATION OF THIS P»GEf<*>.n n-lm Enfr~J
type of equipment. These rates were then used as inputsto the mathematical models. The models could then predictsystem availability which depends on manning level andthe rate of repairs deferred for various reasons.
DD Form 1473. 1 Jan 73
.
S/N 0102-014-6601 SECURITY CLASSIFICATION OF THIS P»OEfW««n D«f« Em;»d)
A Manning and Maintenance Effectiveness ModelApplied to
the Communication Divisionof a
"KNOX" Class Destroyer Escort
*y
Clifford Stephen PerrinLieutenant, United St'ates Navy
B.A., Baldwin Wallace College, 1966
Submitted in partial fulfillment of therequirements for the degree of
MASTER OP SCIENCE IN OPERATIONS RESEARCH
from the
NAVAL POSTGRADUATE SCHOOLSeptember 1975
ABSTRACT
The study objective was to investigate the problems
of ship manning effectiveness, specifically in the main-
tenance and repair areas, using various probabilistic
modeling and data analytical techniques of operations
research. Maintenance and Material Management data from
the Maintenance Data Collection System were used for
estimating failure rates, repair rates and maintenance
deferral rates for each type of equipment. These rates
were then used as inputs to the mathematical models.
The models could then predict system availability which
depends on manning level and the rate of repairs deferred
for various reasons.
TABLE OF CONTENTS
I. INTRODUCTION 8
II. NATURE OF THE PROBLEM 10
III. INVESTIGATION OF DATA 14
A. TABLES OF STATISTICS FROM DATA 18
IV. REPAIRMAN TYPE MODEL 33
A. INPUT ASSUMPTIONS 35
B. SYSTEM STATES 36
1. Finite Capacity Assumption 36
2. Labeling of States 36
C. BALANCE EQUATIONS 38
D. SOLUTION TECHNIQUE 39
V. RESULTS 41
A. SPECIFIC RESULTS 42
1. Optimistic 42
2. Pessimistic 42
3. More Realistic 42
B. RESULTS OF VARYING NORMAL REPAIR TIMES . . .43
1. Graph of System Unavailability VersusAverage MTTR and Manning Level 44
VI. CONCLUSION 46
APPENDIX A List of Acronyms, Abbreviations andEquipments 47
COMPUTER PROGRAM 48
LIST OF REFERENCES 56
INITIAL DISTRIBUTION LIST 57
5
LIST OP TABLES
I. MTTR BY RATING GROUPS OF THOSE EQUIPMENTS REPAIREDIN LESS THAN OR EQUAL TO ONE DAY DURING NORMALREPAIR (IN MAN-HOURS)
II. MTTR BY RATING GROUPS OP THOSE EQUIPMENTS REPAIREDIN TWO TO FOUR DAYS DURING NORMAL REPAIR (INMAN-HOURS)
III. MTTR BY RATING GROUPS OF THOSE EQUIPMENTS REPAIREDIN FIVE OR MORE DAYS DURING NORMAL REPAIR (INMAN-HOURS
)
IV. MTTR BY RATING GROUPS OF THOSE EQUIPMENTS PLACEDIN DEFERRAL REPAIR (IN MAN-HOURS)
V. MTBF OF THOSE EQUIPMENTS FAILING IN LESS THAN365 DAYS FROM THE TIME OF LAST REPAIR BY THERATING GROUP OF THE REPAIRMAN WHO MAINTAINEDTHE EQUIPMENT IMMEDIATELY PRIOR TO FAILURE (INDAYS)
VI. MTBF OF THOSE EQUIPMENTS EITHER FAILING OR EXPE-RIENCING REDUCED CAPABILITY IN LESS THAN 365DAYS FROM THE TIME OF LAST REPAIR BY THE RATINGGROUP OF THE REPAIRMAN WHO MAINTAINED THE EQUIP-MENT IMMEDIATELY PRIOR TO FAILURE OR REDUCEDCAPABILITY (IN DAYS)
VII. AGGREGATE MTBF, MTTR, AND PROBABILITY OF ENTERINGNORMAL REPAIR (MTBF AND MTTR ARE IN DAYS)
LIST OF FIGURES
1. Minimum Path Representation of System Availability
2. Graph of System Unavailability Versus Average MTTRand Manning Level
I. INTRODUCTION
This project was defined and was under the direction
of Professor Donald P. Gaver, Department of Operations
Research and Administrative Sciences, of the Naval Post-
graduate School, in cooperation with Dr. S. Sorensen of
the Naval Personnel Research and Development Center, and
was sponsored by NPRDC. The study objective was to inves-
tigate the problems of ship manning effectiveness, specif-
ically in the maintenance and repair areas, using various
probabilistic modeling and data analytical techniques of
operations research.
The author undertook a pilot study: to investigate
the availability of key equipment in the Communcations
Division of the Operations Department on a "KNOX" Class
Destroyer Escort Ship.
Maintenance and Material Management data from the
Maintenance Data Collection System (3-M/MDCS) were used
for estimating failure rates, repair rates, and mainte-
nance deferral rates. These rates were then used as inputs
to the mathematical models from which equipment availability
could be predicted, as the latter depends upon maintenance
personnel available. Primary emphasis was placed on the
analysis of the available relevant data, which could be
easily manipulated to yield meaningful parameters as input
into the model.
8
The Communications Division is a large system, itself
consisting of many complex sub-systems which fail and need
to be repaired. The entire ship, likewise, may be consid-
ered to consist of several systems, each contributing to
the readiness and availability of the ship for combat;
that is, the ability of the ship to maintain some Readiness
Condition for an extended period of time.
Simplifying assumptions are made in order to reduce
the size and complexity of the system: only those sub-
systems judgementally deemed critical to maintaining
mission capabilities necessary for combat are explicitly
considered as failure-prone and in need of maintenance.
A single carrier Task Group was selected to be the operating
environment, and no other communication responsibilities
are assumed to be placed upon the ship. One hundred
percent availability of the associated equipment periph-
erals was assumed; that is, microphones, patch cords,
antennae and various other items, having spares readily
available and low failure rates.
II. NATURE OF THE PROBLEM
A ship at sea must "be a self-maintaining entity in
order to successfully perform an assigned mission. The
proper manning levels could have a significant impact on
whether or not a ship successfully completes the assigned
mission. This impact could vary with (a) equipment repair
times, the latter "being related to the experience, ratings,
and numbers of men aboard, (b) equipment failure rates,
these depending on personnel skill and training, assuming
that personnel with the proper Naval Enlisted Classifica-
tion to do the work were on board. Equipment availability
also (c) depends upon spares availability. Lack thereof
influences the rate of deferrals.
Representing one component of mission success, equipment
availability in the Communications Division and its effect
on mission success was considered, using the criteria
of the above paragraph. Manning levels and lists of
equipments were then identified, by arbitrarily selecting
a "KNOX" Class Destroyer Escort as a base case.
The USS DOWNES, DE 1070, was used as a prototypic sit-
uation from which to gather equipment loadings and author-
ized personnel manning levels. An Item Designation Report,
Ref. 1., Ship Equipment Configuration Accounting System
(SECAS) Report Number 502.1, was used to determine the
10
quantity and location of the equipments of interest.
Manning levels for the areas of interest were determined
by reviewing the appropriate BUREAU OP NAVAL PERSONNEL
REPORT 1080-14. These equipment and personnel loading
factors were used to provide a basis from which to initiate
the model. Changes in equipment and personnel can be
made in the model, so that (a) sensitivity studies may be
made, and (b) the model may be applied to quite different
shipboard environments.
The capabilities that were considered to be necessary
for combat, and the critical sub-systems for each specific
capability are identified by equipment name and Equipment
Identification Code. These acronyms and names are defined
in Appendix A. The Networks were as follows:
(1) Network Number 1, simplified to an uncovered UHP
transceiver the AN/SRC-20 (EIC - QD3S).
(2) Network Number 2, simplified to consist of an uncovered
UHF transceiver the AN/SRC-20 (EIC - QL3R).
(3) Network Number 3, simplified to consist of a UHF
transceiver the AN/URC-9 (EIC - QD48).
(4) Network Number 4, simplified to be a UHP transceiver
the AN/URC-9 (EIC - QD48).
(5) Network Number 5, simplified to be the (KY-8) and
an UHF transceiver the AN/SRC-20 (EIC - QD3R).
(6) Network Number 6, simplified to be a KV/-7 (EIC -
QP10) and a HP transmitter the AN/URT-23 (EIC - QE1N).
11
The teletypewriter and the HF receiver were not considered
critical because spare systems exist to take the load.
(7) Network Number 7, simplified to an UHF transceiver
the AN/ SRC-21 (EIC - QD3S), KW-7 (EIC - QP10).
(8) Network Number 8, simplified to the KG-14 (EIC -
QPOQ) and KW-37 (EIC - QF18) and a VLF/MF receiver the
AN/WRR-3B (EIC - QBU).
The above capabilities and equipments were selected
for attention as a result of consultations with Naval
Officers who had spent at least one tour on a "KNOX"
Class Destroyer Escort Ship. These simplified specifi-
cations were considered general in nature and related to
the Command and Control mission of this class of ships.
The following block diagram illustrates a minimum path
representation of those equipments that must operate in
order for the system to function. The equipments compris-
ing each block are listed below. Where more than one
equipment is listed below a block, the equipments were
considered interchangeable. Specifically in the first
block, 6 of 7 means that at least 6 pieces of the 7 avail-
able equipments must function for the block to function,
and the block must be operating in order to have the system
operate. The failure of two pieces of equipment in block
one would thus cause the system to fail by this definition,
where in fact only one of the sub-systems has failed.
12
System failure by this definition is the loss of at least
one sub-system.
Figure 1
Minimum Path Representation of System Availability
6
of7
1of2
2
of4
1of2
1of2
3of4
1
of2
QD3R QF1K QF10 QE1N QF18 QFOQ QB1JQD3SQD48
13
III. INVESTIGATION OF DATA
An investigation of the data supplied by Fleet Mater-
ial Support Office was undertaken to determine whether
meaningful repair rates and failure rates could be extracted
for each type of equipment in the model. The data that
were used in this analysis were from the complete 3-M/MDCS
file from 1970 to July 1975, covering all ships reporting
to the 3-M system, on the listed equipments. It became
immediately apparent that the time in man-hours to repair
any failed equipment was easily extracted from the data
source. This was done for all the equipment. On the
other hand, meaningful data on times between failures,
leading to estimates of equipment failure rates were not
as readily accessible; this difficulty will be addressed
subsequently.
One of the initial objectives of this study was to
relate manning levels to maintenance effectiveness, and
thus to the reliability and availability of the equipment.
The data concerning times to repair were further analyzed
to extract the mean time to repair (MTTR) for each critical
rating associated with the Communications Division; i.e.,
ETC, ET1, ETN2, ETN3, ETSN, ETR2, ETR3, RMC, RM1, RM2,
RM3, RMSN. These twelve ratings which reflect the skill
levels and pay grade of the repairmen were then merged
14
into eight rating groups for this analysis. The title
given each group reflects the majority of the repair actions
undertaken by members of that group. The titles and members
are as follows: ET1 - ETC, ET1ETN2 - ETN2ETN3 - ETN3, ETSNETR2 - ETR2ETR3 - ETR3RM1 - RMC, RM1RM2 - RM2RM3 - RM3, RMSN.
Individualized MTTR parameters v/ere computed over all
maintenance actions in terms of man-hours expended during
the repair action for organizational level repair actions.
Then data sorts of successively greater refinement were
made in order to produce more specific information. For
example, MTTR was computed for maintenance actions completed
within one day of detection of failure, between two and
four days, and for greater than five days after failure.
This study was directed toward the on-board mainte-
nance actions that led to a completion of repair. For
this reason, the author chose to utilize only the MDCS
data cards MCE (Maintenance Closing Event) and CSMA
(Completed Shipboard Maintenance Action). The CSMA
record form is filled out by the organization actually
performing the repair. It is used for organizational
level or what is referred to as "normal repair" in this
thesis; whereas the MCE is referred to as "deferral repairs".
In each case the information recorded by the repairing
15
activity is entered in a very detailed format so as to
facilitate data collection and extraction. A complete
analysis of the available deferral data was not pursued.
Neither were the Shipboard Alteration Actions, since they
were not a direct result of an equipment failure, although
they do contribute to workload.
Estimated failure rates, as presented in the RMA
Design Data Bank report, Ref. 2., vary a great deal, depend-
ing on the data used for estimation: from equipment specif-
ication requirements, results of predictions, test results,
to measurements during fleet use of the equipments.
One of the reasons for the variations is that actual oper-
ating time of the equipments in fleet use is rarely known
and thus real-time data can not be accumulated except
under test situations.
For use in a model we have analyzed the previously
described data set (MDCS) in order to obtain meaningful
times between failure on the equipments of interest.
A brief description of some of the complexities involved
in this simplified system might aid the reader in under-
standing the problems involved in computing failure rates
of equipments from fleet (3-M/MDCS) data. Tv/o of the
eleven equipments modeled were without a spare, three were
substitutable for each other and the remaining equipments
had at least one spare available.
16
All data were first sorted by EIC and then by UIC.
Times between failure were computed using several differ-
ent methods in the process of investigating the data.
The author first computed the time between successive
failures of like equipment aboard the same ship. This
v/as done by chronologically ordering the failure dates
on each ship for each equipment and then computing the
desired statistics. This process was done for both failure-
only items and for failures and reduced capability items.
The second method chosen was to investigate each specific
equipment as identified by serial number aboard each ship.
The data were sorted by EIC, which identifies the equip-
ment type, UIC, which identifies the ship or unit doing
the repair, serial number, and chronological ordering of
failure dates and were then used to compute the MTBF
for each equipment by taking the difference between the
I failure date and the (1-1) repair completion date
for each set of qualifying records.
The next fourteen pages consist of statistical summary
tables and explanation pages for each table indicating
what the author thought was important on each table.
The following definitions are used throughout the tables:
MTTR is the Mean Time To Repair as computed from thedata
MTBF is the Mean Time Between Failures as computedcomponent by component
S.D. is the Sample Standard DeviationM is the Sample Size
17
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18
The entries in Table I. are (a) the mean time to
repair each respective equipment by each listed repairman
rating along with (b) the sample standard deviation and
(c) the sample size. The data were sorted to reflect
those repairs taking place immediately by, first, only
looking at CSMA records and, second, using only those
records which indicated repair was completed in a time
less than or equal to one day.
ETN2 and ETN3 rating groups were involved in the major-
ity of all repair actions shown. The mean time to repair
within each similar set of ratings for each equipment
is essentially the same, when small sample sizes are dis-
regarded.
The MTTR from this table were used as input for the
optimistic normal repair rates in the model that is used
to predict system availability. The MTTR in hours indicated
in this table could reflect an immediate diagnosis of
the cause of failure, no delay in getting parts and a
successful installation.
19
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20
The entries in Table II. represent the mean time to
repair each respective equipment by each listed repairman
rating along with the sample standard deviation and sample
size. The data were sorted to reflect only those records
of equipments entering normal repair by only looking at
CSMA records and, second, using only those records which
indicated repair was completed in greater than or equal
to two days and less than or equal to four days from the
discovery of equipment failure. The longer time period
to complete repair of equipment in this case could be
thought of as being the result of a complicated failure
which could not be immediately diagnosed. This is some-
what supported by the fact that in almost every case in
Table II. the repair times are greater than in Table I.,
and in the majority of cases, greater by fifty percent
or more. If the two to four day delay were solely attrib-
utable to waiting for parts, then the man-hours expended
should have been more in line with Table I., since it took
significantly longer, one would tend to believe the
initial premise of a complicated failure followed by a
more involved repair action.
21
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22
The entries in Table III. represent the mean time
to repair each respective equipment by each listed repair-
man rating along with the sample standard deviation and
sample size. The data were sorted to reflect only those
records of equipments entering normal repair by only
looking at CSMA records and, second, using only those
records which indicated repair was completed in greater
than or equal to five days from discovery of equipment
failure
.
The repair times shown in this table are significantly
greater in almost every case than those in Table I., as
might be expected.
What is more suprising is that the repair times in
Table III. are generally less than those in Table II.
This could reflect a delay of some sort on less complex
jobs than those in Table II., either for parts or for
outside assistance, and most likely does since all repair
actions take five or more days even though the average
number of hours to repair the equipment was less than
in Table II. Another point of interest is that a higher
percentage of repairmen of the RM and ETR groups worked
on the equipment under Table III. conditions than in
Table I. or Table II. This could be the result of a less
complex repair action delayed for parts.
23
The main item of importance to notice here is that,
even though the time to complete the repair action was
greater than or equal to five days the LITTR in man-hours
expended is still only from one to seven hours, which
helps support the tenet that a lot of time is spent waiting
for parts or waiting for other specific conditions in
order to get started with the job at hand.
24
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25
The entries in Table IV. represent the mean time to
repair each respective equipment "by each listed repair-
man along with the sample standard deviation and sample
size. The data were sorted to reflect those repairs listed
as deferrals resulting from operational priority, lack
of material, or the necessity of obtaining outside assis-
tance. This sort was accomplished by looking at MCE
records and all repair times.
ETN2 and ETN3 rating groups v/ere again involved in
the majority of all repair actions; however, the ET1,
ETR2 and ETR3 rating groups number of repair actions in-
creased considerably over those listed in Table I. Again,
within broad rating groups the MTTR were essentially the
same. The MTTR entries only reflect the man-hours required
to fix the equipment and thus does not reflect the average
time to complete repair of 64 days for all deferral actions
taken as a class. This large difference in time required
to complete a repair action is thought to consist mostly
of waiting time for parts or outside assistance.
26
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27
The data used to derive Table V. were sorted in such
a manner that only those failures occurring within 365
days of the previous repair action were utilized. This
method tends to give a conservative estimate of the MTEF.
Each equipment type was looked at component by component
so as to get the most information about failure time
from the data; i.e., list all the maintenance actions on
one piece of equipment in chronological order and record
the time between completion of last repair and the next
failure, when the process is out of data on that particular
piece of equipment, start again with the next one.
The data used to derive Table VI. were sorted by
components that either failed or were listed in a reduced
capability status during a 365 day time span from the
completion of the last repair of each component. This
method in general yielded shorter MTBP than those looking
at failures alone, such as on Table V. It should be noted
that the sample for each catagory in this table includes
the complete sample used in Table V.
28
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B m •st CM NO CV rH CV -sf 01 a^ori cv in st CO st cm f_ ^ J-. ^ fH ^ rOO1 rH O rH O rH CM xQ O rH CM c- C^ jj p 2 3 p -j d< rH H rH rH rH r-i rH rH rH rH &
fA T-i *ri *ri 'rt *H Oog aj crj crj crj cj cc! (-1
CO in rH in vC in -<t cv £— CV CM On vO in CM CV CM CM fjH Ji. Ci, Cx, tc-i ^-i P->o »"5 -M-xO ON O O m in xo xO O C<\ rH s CO cv CO xO rH sto 1-1 • • • • • 'r-i • • rH • . CV • • CV •
< PQ O rH ON xO CM CV CV CO xC O On 003' CV
rH rHrH O-rH
rH CM On CO rH st On 00 r-i CV CM st in xO O
O co
S£ Pm Ph Pi PJ as PiH O m • en • Eh • Eh • Eh • Eh • •
crf o EH rH Eh CV Eh CM Eh -st 6h in Eh xO OVrH
*U S 23 ^~t
30
Table VII. is the most general table of all, and could
quite possibly contain the most enlightening information
also. Rows one and two are straightforward MTBF in days.
Row three entries are the mean time to complete a repair
of a failure for all actions listed as organizational
level and ready for immediate repair. A range of three
to thirteen days makes it rather hard to believe the
often quoted MTTR in terms of hours as indicated in
Tables I - IV. It should also be pointed out that over
75^ of the observations were actually less than each of
the respective MTTR computed which is also indicated by
the large standard deviations compared to the location
of the mean.
If times to repair were exponentially distributed,
one would expect 1 - e-U/MTTR) (MTTR) = Q>63 Qr ^
of the observations to be less than the MTTR, this along
with the larger standard deviations lend support to
saying that repair times tend to be "hyper exponential",
having very long tailed distributions.
Similar reasoning may be applied to row five, which
contains both failures and reduced cabability records.
Rows four and six depict deferral type maintenance infor-
mation on the MTTR for each respective equipment. One
could infer that these long MTTR in days were the result
of waiting for parts or outside assistance.
31
The probability of entering normal repair as listed
in row seven was computed by summing over all maintenance
actions of each equipment type (different EIC), the total
number of MCE (deferral repair actions) and the total
number.-of CSMA (normal repair actions). The entry in
row seven was then computed to be CSO./ (CSMA + MCE).
32
IV. REPAIRMAN TYPE MODEL
Individual pieces of equipment can fail and either
enter normal repair or enter deferral repair with some
specified probability for each type of equipment. Equip-
ment failures are repaired on a First-Come - First-Served
basis. If a failure occurs and is not repaired, the system
is subject to failure. When enough failures occur so
as to saturate the available number of repairmen, a repair
queue begins to build up of those equipments waiting to
be repaired. Equipments which can not be repaired due to
lack of material (parts) or lack of technical expertise
are placed in a deferral repair status and generally
experience an extremely long delay before the situation
can be remedied.
The deferral repair time distributions from Table
VII. could be used as parameters not really dependent
on the number of repairmen available and thus can be con-
sidered in service concurrently with the normal repair
actions. Thus a generalized view of this model is that
when equipment fails it is either repaired quickly or is
delayed for some reason. The probability of being in
any particular situation is an output of the model developed
here.
33
This model is based upon a simplification of the main-
tenance process and is designed to utilize the results of
the data investigation of Chapter III, or any other varia-
tion a user might desire. One, two or three repairmen
may be specified to work on any number of equipments.
The model is more realistic than other repairman type
models in that it allows for individualized failure rates
and repair rates for each type of equipment. Different
deferral probabilities for each equipment are also allowed,
These additional features of the model, while increasing
the realism of the problem, also increase the complexity
of the solution as indicated by G-aver in Ref. 3.
Incorporating manpower data and equipment reliability
data into a model was predicated on considerations in
three major areas:
(1.) availability of sufficient and meaningful data,
(2.) ability to vary factors of interest to Navyplanners,
(3.) measures of system performance.
Availability of data has been previously discussed
in Chapter III. Factors of interest to the Navy planners
were manning levels, manning effectiveness and equipment
reliability and availability. The effect of changed
overall manning levels on mission success can be studied
by using differing numbers of repairmen in the model.
34
The primary measure of system performance was taken to
be the probability of mission success, or one minus the
probability of mission failure.
A. INPUT ASSUMPTIONS
The individual times between failures, times to
complete repairs, and times to complete deferred repairs
are assumed to be independently and exponentially distrib-
uted. This assumption seems credible as indicated in
Chapter III, where the number of observations examined
was greater than three to four hundred. Basic parameters
appearing in the models are the MTBP for equipments as
well as MTTR (normal, and deferred).
Each equipment fails at a different but constant rate
F. (i=l,2, . . . ,N) , and can be repaired at the normal
(immediate) repair rate R. (i=l,2, . . . ,N) or at the deferral
repair rate RD. (i=l,2, . . . ,N) . Each equipment is assumed
to go into immediate repair with probability p. or deferral
repair with probability q.=l-p. (i=l,2, . . . ,N) . These
rates and probabilities were determined from the data of
Chapter III.
Deferral repair action MTTR over all equipment types
ranged from 54 to 92 days to repair a failure. This
long time was thought to be a result of waiting for parts
or outside assistance. The MTTR computed here was so
35
much greater than the MTTR for normal repairs (10 to 60
times longer) that the author decided to use the MTTR
for deferrals as a repair time not influenced by actual
repairman time. In other words, deferral repairs could
be going on simultaneously with normal repairs even though
all the repairmen were busy. This is due to the long wait-
ing time involved in a deferral action relative to the
actual time required to fix a piece of equipment.
B. SYSTEM STATES
Normally, order of failure is important in determining
when an equipment begins to get repaired. This has not
changed in this model, the first item to fail and enter
into the immediate repair queue is serviced first. In
practice a priority scheme might be followed.
1. Finite Capacity Assumption
Three failures of any type are all that are allowed.
This restriction can be changed by incorporating additional
echlons of state spaces into the model. Allowing only
three simultaneous failures was considered adequate,
since only eleven or twelve pieces of equipment were modeled
as a sub-system.
2. Labeling of States
The order in which failures occur define the
label of each possible state for the system to be in.
36
The states of this model may be identified according to
the following format:
N is the number of different equipments labeled from1 to N.
i/jA (i,j,k=l,2,...,N)
(o) no equipment failures
(i) equipment number i has failed and is innormal repair
(iD) equipment number i has failed and is indeferral repair
(i,j) equipment number i has failed first and isin normal repair, equipment number j hasfailed second and is in normal repair
(i,jD) same as (i,j) with j in deferral repair
(iD,j) same as (i,j) with i in deferral repair
(iD,jD) same as (iD,j) with 3 in deferral repair
(i,j,k) same as (i,j) with equipment number k hasfailed third and is in the normal repairqueue
(i,j,kD) same as (i,j,k) v/ith k in the deferralrepair queue
(iD,jD,k) same as (i,j,k) v/ith i and 3 in the deferralrepair queue
(iD,jD,kD) same as (i,j,k) with i, 3, and k all inthe deferral repair queue
State (3,4U, 7) would mean that equipment number 3
had failed first and is in the normal repair queue, equip-
ment number 4 had failed second and is in the deferral
repair queue, and equipment number 7 had failed third
and is in the normal repair queue.
37
Each piece of equipment to "be modeled is assigned a
unique equipment number and thus if there are several
pieces of the same equipment, each has a unique number
even though the failure and repair rates are identical
for each equipment.
C. BALANCE EQUATIONS
The balance equations equate the rate at which the
system enters a certain state to the rate at which the
system leaves that state. Now using the previously defined
states and parameters, the following balance equations
for two repairmen are written as a selection from the
entire system. Where, as an example, P!T1
. means the
probability of being in state (j'D,i). The total number
of states is equal to 1+2(N)+4(N) (N-1)+8(N) (N-l) (N-2)
for this model.
N N N
<iti *±> Po
=i?l R
iPi
+ifl ra
iPi
N N N(R. + S. F.) P. = P p.P. + %j. R.P. . + .§. RD.P.^ .
This is to say that the only way to get into state
(i) is to be in state (o) and have equipment i fail and
go into normal repair or to be in state (j,i) or (JD,i)
and have equipment j repaired. The only way to leave state
(i) is to either have equipment i fixed or to have a failure
of another equipment.
38
N
< Ri +HJ+ 0) Pi(jfk
-PlfjVk
Only allowing three failure yields the above equation,
since there are only two repairmen.
(RD1
+ RDd
+ RDk ) piD);jD(kI)
= PiD(jI)1k
Pk
Here it is noted that three deferrals are being ser-
viced even though there are only two repairmen. This is
due to the assumption about deferral repair actions.
D. SOLUTION TECHNIQUE
The Gauss-Seidel iterative approach to the steady
state solution of a system of balance equations was used.
Briefly, this approach is as follows:
39
1. Initiate Starting State Probabilities
, The most convenient assignment method is to use
an equally likely distribution and assign each the value
1.0/(total number of states).
2. Turn the Crank
Using the present values for each state, solve
for P and use the new value for P when solving anyo o
additional equations containing P . This same method is
then used for P-, and all of the other possible states.
Continue until a new probability has been computed for
each state.
3. Normalization
Take the sum of all of the new probabilities just
computed and divide it into each of the new probabilities,
thus 'ensuring that all probabilities add to unity, as
they must.
4. Check for Stopping Criteria Satisfaction; Re-iteration
The author chose to use a relative ratio method
to test for a minimal change in probabilities, since many
of the probabilities would be extremely small and would
thus always pass a simple differencing technique. The
method was to take the absolute value of the difference
between the old probability and the newly computed proba-
bility and divide by the new probability. (I OLD-NEW|/NEW)
This was done for each state and checked to see if the
40
result was greater than 0.0001. If so, for at least
one state, the iterative process must continue until
all states pass the stopping criteria; i.e., GO TO 2
and start again.
V. RESULTS
The model was programmed in Fortran G and was executed
to generate the results listed here. The computer listing
follows Appendix A. The output of this model comes in
the form of long run probabilities of being in any partic-
ular state. Selected sorting and summing procedures
are then used to produce the probability that any set
of equipments are down, and thus it is possible to calculate
the probability that the system is down. This was done
for each of the sets of equipment described in Figure
2 and then the joint probability was computed and used
in the results. As an example of the size of the sorting
and summing task: using N=12 equipment yields 11,113
different possible states which are then easily sorted
and summed on a computer by user supplied logic statements
specific to the information desired.
The author chose to present two of the multitude of
possible outcomes in the Results section.
41
A. SPECIFIC RESULTS
1. Optimistic
Using the normal repair times (Table I.), proba-
bilities of entering normal repair (Table VII.), and the
deferral repair times for failures (Table VII.) resulted
in the following:
Probability that all equipment are up = 0.4220
Probability of system unavailability = 0.1185
Where system down means that at least one sub-
system or mission capability can no longer function due
to equipment failure. It should be pointed out that the
other seven sub-systems could quite possibly be available.
2. Pessimistic
Using the normal repair times for failures (Table
VII. row 3), and keeping all other parameters the same
as the optimistic case.
Probability that all equipment are up = 0.0988
Probability of system unavailability = 0.3086
3. More Realistic
A weighted average of times to repair each equip-
ment was used to compute the MTTR used as input for this
calculation. The method of weighting was as follows:
(1) sort the data to reflect only normal repair records;
(2) extract a frequency distribution of the number of
days to repair a failed equipment;
42
(3) use this distribution to compute the weightings
for each of the equipments. The time-to-repair factor
for the one-day-or-less category was the time in hours
from Table I. times the percent of normal repair actions
occurring in one day or less. The time to repair factor
for the two-to-four day category was 48 hours times the
percent of normal repair actions in that category. The
time to repair factor used for the five-or-more days
category v/as the MTTR for failure-only undergoing normal
repair from Table VII. Since the MTTR was listed in
days, it was converted to hours and multiplied by the
percent of normal repairs occurring in five or more days.
Generally the percentages for each category were about
65/£ in one or less days; 10fo in two to four days; and
25f° in five or more days. The results of using this
input was as one would expect, in-between the optimistic
and pessimistic cases.
Probability that all equipment are up = .3025
Probability of system unavailability = .1543
B. RESULTS OF VARYING NORMAL REPAIR TIMES
The following graphs were made to show the complete
range of good to bad repair times and their effect on
mission failure.
43
Figure 2.
Graph of System Unavailability Versus Average MTTR andManning level
P
12 3 4 5 6 7
AVERAGE NORMAL MTTR IN DAYS
The numerals nearest the lines indicatethe number of repairmen used.
44
Figure 2. presents both equipment sets using 1,2
and 3 repairmen, over the full range of optimistic to
pessimistic values for the normal MTTR. There appears
to he very little difference in results between using
two or three repairmen on Equipment Set 1 and thus two
repairmen would be preferred. There v/as essentially no
difference in results between the differing number of
repairmen on Equipment Set 2 and thus one repairman would
be preferred. The realistic estimates for these sets
of equipment varied from; a IJTTR of 2.75 days and a system
down probability of 0.08 for 1 repairman to 0.07 for 2
or 3 repairmen on Equipment Set 1, to a MTTR of 0.88
days and a probability of the system being down of 0.09
for 1,2 or 3 repairmen. It v/as noted that 1 repairman
on Set 2 produced very slightly better results than two
or three repairmen; this v/as considered to be a result
of computer roundoff error since there was essentially
no difference between them.
45
VI. CONCLUSIONS
Useful failure rate and repair time parameters can
be extracted from 3-M data. Simplified systems of critical
equipments and the associated repairmen can be modeled
to estimate a specified mission probability of sucess.
The long time to complete deferral repairs are basic-
ally the limiting factors in computing mission success
or failure; i.e., the probability that the system is
down reaches a limiting value does not decrease no matter
how fast an item can be fixed in normal repair. This
would seem to imply that in order to get more equipment
repaired faster, the deferral repair times need to be
reduced.
This model can be expanded to look at cases allowing
more than three failure quite easily, the only note of
caution is that as additional failures are included the
number of possible states increases too, which may at
some point become too unweidly to handle.
It is the author's recommendation that further investi-
gation into simplification modeling of systems be looked
at in other areas in an effort to reduce modeling costs
without sacrificing the desired goals of the Navy planners.
46
APPENDIX A.
List of Acronyms, Abbreviations and Equipments
CSMA
EICHFMCE
MDCSMPRCVRUHFUICVLPXCVRXMTR
Completed Shipboard Maintenence Action(Normal Repair Form)Equipment Identification CodeHigh FrequencyMaintenance Closing Event (DeferralRepair Form)Maintenance Data Collection SystemMedium FrequencyreceiverUltra High FrequencyUnit Identification CodeVery Low Frequencytransceivertransmitter
EIC
QB1JQB3AQD3RQD3SQD48QE1NQFOQQF1KQF10QF1BQ33K
Equipment Name
AN/WRR-3BR-1051AN/SRC-20AN/SRC-21AN/URC-9AN/URT-23KG-14KY-8KV/-7KW-37AN/UGC-20
Function
VLP/MP RCVRMF/HF RCVRUHF XCVRUHF XCVRUHF XCVRHF XMTRSECURITYSECURITYSECURITYSECURITYTeletypewriter
47
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55
LIST OF REFERENCES
1. Ship Equipment Configuration Accounting System ReportNo. 502.1, Item Designation Report on DE-1070p. 1-150, 6 June 1974.
2. Naval Ship Engineering Center, Reliability/T.-aintain-ability/Availability Design Data Bank Report,p. B-l - B-33, March 1974.
3. Naval Postgraduate School Report NPS55GV73021A,Analytical Eodels for Supplementing Ship ManningSimulations, by Donald P. Gaver, p. 9-13, February1973.
56
INITIAL DISTRIBUTION LIST
No. Copies
1. Defense Documentation Center 2
Cameron StationAlexandria, Virginia 22314
2. Library, Code 0212 2
Naval Postgraduate SchoolMonterey, California 93940
3. Department Chairman, Code 55 2
Department of Operations Researchand Administrative SciencesNaval Postgraduate SchoolMonterey, California 93940
4. Professor D. P. Gaver, Code 55 Gv 9
Department of Operations Researchand Administrative SciencesNaval Postgraduate SchoolMonterey, California 93940
5. Mr. E. Ramras jj.
Dr. R. Sorenson ±
Dr. J. Silverman 1
Lcdr. C. Helsper 1
Dr. S. Sorenson 1
Dr. R. Holzbach 1
Library 2
Naval Personnel Research and Development Center
San Diego, California 92152
6. Professors P.R. Milch 1
K.T. Marshall 1
P.A.W. Lewis 1
J.D. Esary 1
Naval Postgraduate SchoolMonterey, California 93940
7. Dr. J. P. Lehoczky 1
Statistics DepartmentCarnegie-Mellon UniversityPittsburg, Pennsylvania 15213
8. LT Clifford Stephen Perrin, USN 2
1236 Spruance RoadMonterey, California 93940
57
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DUDLEY KNOX LIBRARYNAVAL POSTGRADUATI SCHOOLMONTEREY. CALIFORNIA I
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PerrinA manning and main-
tenance effectiveness
model applied to the
communication division
of a "KNOX" class
destroyer escort.
thesP3396
A manning and maintenance effectiveness
3 2768 001 00229 8DUDLEY KNOX LIBRARY
