Re iris t a Colomb ian a de'iII(//ell!ll/irrlS

Vol. IX, (1975), pd g s . /(, / .. l " /

NEW TENDENCIES IN INDUSTRIAL STATISTICS: IS SQC IN A CRISIS?

by

Viorel cs: VOD'A'

Motto is Statisti"cs an academic tool?

a tocl is not an end in i t s e l F"

J. M. Hommersley

I. Introduction. Sometimes, [nd ust r ia] Statistics have been considered by some

pcopl eus a ('ollection of s impl c <t.u ist ic-a l f echn iqu es appl ic d to certain pecu l iar

problems raisl·d from industrial .u-t iv irv

Commonl~", lndustr ia l Slati,.;li,·,:; i" 'ls~c){'iat('d wi ih ihe app l ica t iou of :-;onll'

test" -- as d ist aucc tests for testinl! normality- t or F-leSls, l'it t inp siraightlines

or ,.;onlf' l'urq:" or wr it ing some modcls in Analysi:-; of Variance.

Thl' re ]ut ivr: simplicity of con t ro l (,harts iu Stat istical Quality Control (SQC)

has accredited also the he l icf 'hat iu fact [n dns t r iu] Statistics are a I iIIit' hit "Io\\'

malhematic',," •

The bituation is nol at all just ,'"'It. III 1';1('1, lu(lu,"trial St,lIi"lit,,:-; li\.;(' all :-;1,,-

:i') Ce m cr of Math ern at ic a l Stillislic:--, Hucharc:-.t- Rorn ani a. NII\\ eXt!lilllgt· \·i ....ir o r un d c-r

(;rant of Nt\~ at [l n ive r x i t y of C:"liforni", Ht'rkcky, 'Jj-20.

Ii li('al IIlI'lh"dol"!2'\ i,..;a hod) 1'01'o!>lailling kllo\\led;;l' 011ac-t uu l I'hl'1I01ll"IIa - in

Ihi" """lOll illdU,";lrial I'ro('l's"{,,,.

Through 111<11111'"'''I i ..al I.rail <'II 1''', ~1<1lisli('s hu...; a";lll'cial placc dill' 10 i t s

,.;,ro IIg i III (' I' 1'1'1'('II<' I' \\ j Ih I' rar- Ii ..I' •

.\ "did s lut ixt i..al r!''''(''IITh al wav « vvi l l Iry 10 sol vc a('llla! probl eru I" 1'011";-

t.ru..1ill!!', illlpro\ iu;; or just ,.;imply using a math c mat ic al modrl , 1'1111101to coustrur-t

I'irsl a JlIod('I and t lnn look 1'01'1 1If' nppro pr i.u e prohl cm - \\hich o ltr-n lIlay 1101I'"i"".

(Sec rdCn'1l1'('''; SI'CI iOIl A ).

TIlt' pUl'pose or IIH·...;(' l iue s j" 10 e mph as izc- "'o",e new lend('npif'''' and pos.s ihle

I'lllurl' nuu h c ma t i r al lools in [n d uxtr ia] S'ali"til's. Since th e ma t t rr is so largf', \\C

,.,hall siress c sp rc ial lv on S()L

2, Recent 'len de nc ies . II' ."011l('0I1('follo\\'s carl·l'lIlly th o l iterru ur e publ ish cd

ill Ih(' m u t tc r la'" 1('1l year"" h.. w il ] o(,"'cl'\l' th at :

a, I.ik I(,.-;Iill;; all 1'1 rr-I ia lri l i t y I,·chuique,.. h avt- r ecc ived a trcmcn dou s d('\clop-

n](·III. ThrtlU!!h Ihe maill lopie,.; \\(' \\ill cniisl :

;lc ..e"'rat ..d lil'(' 1,-",1."

c",li!llalioll 1'1'0'.1"111'-'I'nlll1 JlIlllli ..ellsorcd sa"'pl,'",

n,li,tllilit\, or """,pll'" "\,.;1(',,,'" ill l'onnl'('lioll \\jlh dl'lll'llIlelll "'ul''';~'''''''111 I'ai-

lu 1'(''"

lIe\\' di,-arilllllion I'un.. lion." a" lillie-Io- failure dislribulioll";

a\';lilaIJi 1 ity 'h ('ory

I'aull - In',, - aualy"i"', a",", o.

(Sf't· IT f('j'('nI' ('''; , S("'I ion B )

11. In S()C Ihe 1I\;ljorily 01' \\()r~", an' Oil a"" ..planl'('"amplillg lechniqucs, l''';-

pecialh Oil 1III1IIi"I,· sallll'lill1! all" Ba"'siall 111"1100".'"(....,'" r..r.-I'I'II("·S, ~"('Iioll CL

1.0""1";11""111,aria",,"s, 1III1IIi,arial'· "01111'01..!"'I'IS, II"" of S"",,' uuxil ia r "i,..ll'i-

hu t ion s - lik,' Hurr dislrilHilioll- fur ,'ollslrtJ('lilll! "ltarls for larf! ..sl alld slIIall.- ...."

sallll'''' ,allies ill a normu l pupu lut l on, a.soo. (se,' refel'l'II<"'s, S"eliull IJ).

Tit is s it ua t iun ha s impl cuunn-d IIIl' id ea - eSl'ecially ill Ellrup"- lloal Sl)C i....\

ill a .... risis .. , till' ,.'oml'lIl,'rizalioll all,1 aur onuuion lJeill!; two fa,'lors \\It idl \\ ill

.. l iminut c gradually e-l ass ir-a l control ch art s, lite mai n at tc nt iou rClliainillf! "OIW"II-

t rat r- ,1 Oil 1{,·liahilily, Sampl ing Plans and Mlllli' ur iat« Slatislical [,,"lroL Tit i....

idea h a....a silllple hUI not a very ohv iuus ,'xplallalion:

In Spil" of Ihe elTorls paid 10 find more ....0l'lti,.,li,·aled louis ill ('olllrol -'!JaI'ltheo-

ry, the ..Ias,.i"al She\\'harl ,'ul1lrol dlarls art' ,.Iill the mos t elTi r-i"1I1 inslrllllll'lIl for

oluu in illg a ..Iuse innlf!c of a !,rm'e,,;,. cvolut iou,

(.ollll'"tl'rizalion and aut omat iun han; given a va luuhl « 111'11' 10 S!,ll: all,lllw ,i-

....lIalizalioli of ('onlrol "'nHls Oil '1'\' sels do,·...1101IIlt'all Ilteir "i.Sllli ...sillf!·,

II is imporlanl 10 nol" thaI all alllOlllali,' ("I' 1'1"l'Ir"lIi ..) ""lItl'ol ,I", i,'(' illsla~

"u"l hUI nol on Ihe proe,',.,s ..'ollliion (sc" rl'f'·I'I'II'·('s. S""lioli 1:),

Tlw ""oluI.ion ma" he pllrsll"" only if one U"('S a .slalisli,'allll('lltodol0f!y ""'1

if litis on" is an aulolllaliz,'." 0111'•

.\ ....a pra"1 inti 10111)'llI',,!:ar' "0111rol ..ltarls s"l'lIll'd 10 ",' 11111;I 110\\allllost 1"'1'-

f"cl, all,1 afler soml' illlprmTmenls (SI'" refl'l'I'll<'es, S..eliull II) !lOlhilig Itas 1""'11

adde" "ilholll a Ius.'" of silllpli"ily,

Thi" mav I...an I""planalion of the poinl (h). 0111' Ihing \\1' ha v e 10 noll': an

ill'l,orlanl "'I'p in cuntrol .-h art s pr ao t ice is the interprdalioll of 'hose charl".Thi"

iu n-r pr c ru t ion i" a ('olllhination of "cil'ncc (t,nl!ilH'erinl! tfJinking) and art" ("kill"

lu 111011..1' analu!!il"" \\ i t h IHI" iou s c'ases meI a.s.o.) wh ich is in a \\ay 1II0re impur-

e qn ipm e n t reli ab il it v (see Bl'f('l'ences, Section n, [10 ll,

And IIIl' process con tr ol by the aid 0/ control cb ar t s is the key to all kinds o]

.11 is useless to app lv c'omplicated rel iuhi l ity and lifelesting t ec hn iques on

prod III",!" del iVl'rcd-hy a proc""s wh ich is not we l l dominated.

A nat uru l !!I'nl·.ral 1'10\\ of hc)\\ things must he done seems 10 lH' thl' Iol low ing :

Raw Macerial)

Production LinesAcceptance

Sampling

,

t nt e ricrotion be/ween Q and R me t h ods

Oesing and

Research ....on Q and R

CustomerInformation

Department

l:igure 1

Finite Acceptance

SamplingProduct s

SaleLife - t est ing

and~------lReliability Pro-

cedures

masterpiece) in our opinion"

*) In this field, the lIandbook of SQC edited by Western Electric Company IS still a

164

01" "Irion .....kind ...; (pi('!','s, hu l k, a,..;.o.) as 1\('1\ as 10 lin ill' prodn'·I ....."II ie,II also

mav lit' dl,li\"'rl,d in dil"krl'nl "a~s, I.a ....."ont'('nlrall'd II", alll'nli"n 01" '';Ialislil·ii''l.~

may in t eruc t , providing cuc h 011.('1' \\itll i,kas or .....pl'l'il"i" anaIYlil'alllll'tliuds.

Attending Ibis fall a course in Ad vauccd Bpliability Tl.pory hc ld by I'rofpssor

R. E. Barlow at the University of California, Berke lev, se'ems 10 t he presenl an-

thor that the tool of so -c al led "isutunic regression" cOI~ld b" a useful instrum-,..~~' ........- ........~.....~ }""~

eut not only reliability problems hUI also in Qnalil), Control.

Briefly, the isotonic rel'res",ion proh lcut ,'on",isis in finding

M in im um o]kL

i = 1

2tg . - Xi ) Wi

I

in the condition Xt' < x . "ben i : j wlu-r« ::; "is a partial urdc'rillg on n- J

11,2, •.• , k I and wi> 0 and gi (i = 1, ... , k) arr f!i,,'n. (SCI' Barlol~ and

Brunk, Se~tion E, [441),

In a recent book (Har lov,, l3arlhololl1c"" !3rPllluer and Brunk S('l'lion E, [t\.4I)il

has he en shown t ha t the isotonil' reprl'ssion sol\ ('.S also .....0111(' rr: .....trieted III ax iuunn

like l ihood estimation prob lerus,

This fact may suggesl im mc d ia tv appl ir-a i iun s in [n du s tr ia] Sialistics

Ex ample 1: Consider for instance rho 11101111)' il\nag'I' produclion 01" u l'l'rtain

I i « I . ... , 12 and let us know that rh is prudu ctiun basI' anI in a ypar- say, Ili'

heen constantly inerl'asl'd from monlh 10 1lI0ntll, that is :

165

(2)

In Ihi,.; ";IV,' thc {/ pr ior i knowledgl' on ordering, required by the isotonic regressioll

The pnrposl' is now to {'slimate the monthly average produr-t ion

I" [a c-t , we h avc 10 cou s truvt - ill the assumption of normality- the likl'lihood

lurut iun :

L12 ,- (V 17i

i~ 1 (J \{2; e x p -(3)

and th e n to maximize L --uhje c t to (2), where IIi is the sample size of Xi (sam-'

I f· I .th I ) d' 2. I . I' I I' I k I' .p e 11'11'<1110 I 11' I mont t an (J IS tne variance WIll' 1 or tIC sa e 0 slmp-

l ic ity has been assumed to he the same and known.

An e quiva leu t prohl cm is that cons ider ing \ an average quality of a cert ain

quality characteristic. Thc formulation changes in minor points.

No\\' the open problem is that of finding conlrol procedures for an average qua-

Iity subject to an order restriction.

Example 2: Suppose that a production l in c under sj at iat icul control delivers

hatches of finite prorlur-t s , At the final control station, from e\ery hatch are {'x-

iTacted samples of s ize Ni and suppose that ni defectives arc detected in the

sample of size Ni '

Assigning a Po is son law, we have hence :

Prob, I X.I

11£11i I= (Ai Ni) i=1,2, ... , k , (4)

where Xi i" the handled variable and Ai is the Poisson parameter which has

(5)

Maximizek[Jioo I

-A,N(' I 'I

II, 'I'

(6)

buhjei'l 10 ('») •

The prolrle m has a \Try elegant solulion in terms of isot on ic rr: rre ss ion theory

(see BarIo« aud [hunk, Se('1iun E [44], TIIl'ol'cm 3.1) .

The open problem i,'"' similar 10 that expressed in Ih(' above example

4. Conclusions. Guing back 10 the ques t iou [n Ihe liile : "i,,; SOL in cribi,.;'t';

onr answe r is positively NO and I\(' hc l u-ve the mot iv a t ion 01' IIiis ans wr-r does

nul need more argumenlat ion.

On Iy a lu-st poin t 1\(' like to ,.;Iress : ..." lon~ a,sTcehnol0t!Y \\ ill e"ist (and it

s('ellls that no rra sous are againsl ') it \\ ill [)('ed a tool 1'01'ob,serving ~Ind J,-.'eping

it nndel' control. Compntel's are a major aid in doint! ih is. I~ut i.lr-n t i lic at ion , dc-

liu it iun and invesligalion uf a pract ica l or IIi('or,'lical prob lr-m is st i l l an arlo/'nd

I\'(' hope the art is still only a bnman·attrilJllte.

N. B. Tbe references are !!i\cn in ,.;n(·h a \\a) to he lp the rcurlo r to rl isr-o ve-r

ca",ily tuucb('d areas In the t cxt,

.\ Cs e u e rn]

I. de lLn et t i, 13. (I974) : Bayesiallism : l t s ullifyiug role for botb the [ounda t ioos

au d aj>plicflli()J/s of statistics. 151. St o t , Rev .. Vol. 42, No.2, p p , 117·130.

2. I/amml'~sley. J. M. (1974): Slalistical Tools. ti; Statisliciall, Vol. XXIII. ,~o

2. pp 89·j()6

3. Krns e al . W. (197·j.): The uh iq n itv of st atis t i c s . The American Statistician, \-ai.

28, No.1, pp. 3·6.

4. Narllla. S. C. (1974) : Syslemalic !rays to ideutify research prohl e m s /II s ta t is

tics. lo s t • Stat, Rev., Vol. 42, No.2, pp. 205·209.

B. Re liab iliry .

5. Barlow, U. E. audPro s cba u, I;. (1965): fIlatbematical 'lb eory of Re liab il it v:

John Wiley and Sons, New York.

6. Barlou-, U. E. au d Pro s cbau, F. (1974) : Statistical Theon' of Rel iab ili t y and

Life - Testing Probability fIlodels, Holt, R inehort and Win stan, Inc.,

New Yar.k,

7. Britn ey, R. R. (1974) : The reliability of c om pl ex syslems uritb de pe nd e o t sub

system [ai lur e s : an ab s orh in g .lIarko/} cha iu model. T.echna011etrics, Vol. 16,

No.2, p p , 245-250.

8. Cie ch anouic z , K. (19691: Geueralized Gamllla Dislrihlllion an d Pouer d i stri >

bu ti on as failure di s trib ut irnrs of the compoueuts (doctoral thesis). Institute

of Automation, Polish Academy of Sciences, Warsaw (in Polish) .

9. Engelhart, ~1. aud Bn i», I .. J . .(I973) : Some c om pl et e and ce n sore d sampling

results lor t be Weihull or EXlremeualue d is trib ution, Technometrics, Vol.

15, No.3, pp. 541·550.

to. Fu s se ll, J. B, (1973) : Fault-tree analvs is-» c onc e p ts an d te cbni qu e s . Proc e-

e d in g s, NATO Aduanc ed Study, Institute on Generic Techniques of system

Reliability Assessment, Liverpool, England.

11. Green, A. E. and Bourne. A. J. (1972): Reliability Tecbuology, John Wiley

and Sons, Interscience, New York.

Ifill

.12. Nelson, W. (/968) : A statistical test lor e qna l itv ,,/ t iro ai-ail ab il iries, Tech-

nometrics, Vol. 10, pp. 594-596.

13. Sil/gpl/r1NIlla. N, (1973): 111/('r('nce [ro m a c c e l era te d l i]« t e s t s us iu g Arrbeu i us

tVpf? re-trarame tri zat iou .

l-i . Stormer, II. (1970): Mathelllrlfical Thf?ory 0/ Re l iab i l itv (;nlll{/II). Oldenburg

Verlag, Munich.

C. Acc ep ta n ce Sampling.

15. Bray. D, F .• Lyon, D. A" an d Burr, /. (1973) : Three class at t rib u t e p lan s ill

Acceptance Sampling. Technometrics, Vol. 15, No.3, pp. 575-586.

16. Elder, R. S. (1974): DUlIble sampling lor C+ average, Technometrics, Vol.16,

No.3. pp. 435 - 440 .

17. Shah, D. K. and Pb aiale, A. G. (1974) : The maximum likelihood e s t im at e 0/the [r ac tiou defective under curtailed multiple sampling plans, Technometrics,

Vol. 16. No.2, pp. 311-316 .

18. Valentin, F. M. (1970): Bayesian methods and quality control, (French), Metro,

Vol. I X, No.2, pp. 261-278.

D. Process Control,

19. Austin, J. A" Jr. (1973) : Control chart constraints for largest an d smallest

in sampling from a normal distribution using the generalized, Burr distribution,

Technometrics, Vol. 15, No.4, p p , 931-934.

20. It ou gla s, W. A, S. (1967! : Process control --key to equipment reliability. Pro-

ceedings, 1967 Annual Symposium on Reliability Washington, D. C., pp.267-

272-21. Hillier, F. S. (1964): X - chart control limits based on a s nia ll vtuntb er 0/ s uh-

groups, Industrial Quality Control, Vol. XX, No.8, pp. 24·30.

22. HillierF, S. (1967): Small sample prob ab il it y limits for the range chart, J.

Amer. Statist. Assoc., v e t.. 62. No. 320, pp. 1488-1493 (Correction note: ~.

A.S.A., Vol. 63, pp. 1549-1550)"

23. Mukherjee, S. P. (1964): Economically optil/IIIIII Control limits /01' X-CbrITIS

Calcutta Statist. Assoc. Bull., Vol. 11, No. 49-50, pp. 59-70.

2.L ,lllIkherjee, S. P. (1967): Joint control/or mean an d rarianc e 0/ a normal POptl-

la t ion : Co l c o t i o Statist. Assac. Bull.. Vol. 16, Na. 62.63, pp. 93·102.

_'5. r/~ (Ll ire ira , J. J. and Littauer, S. B. (1965): Control charts uitb doub !e limits

a ud rnus (French), Rev. Stat. Ap p l , , Vel. XIII, No.2, pp. 61·73.

26. de (Lliue ri a , T. J. and Littauer, S. B. (l{)66): Techniques /01' ecouomicall/se

0/ c outro l cb art s (Fre ucb ), Rev. Stat. A'ppl., Vol. XIV, No.3, pp. 43·53.

27. t i at e l , 11. L (1973): Quality Crm tro l mretb od s /01' multivariate binomial and

/JoisS(JI! dis t rib u t i on s . Technometrics, Vol. 15, No.1, pp. 103·112 (good re-

ferences on multivariate quality control).

28. Weil/dling, J. T, (1967) : Statistical pruperties of a general clas so] control

cb arts treated a s a Markov process. Ph. D. dissertation Ce lu mb io Universi·

ty, New York.

29. l'Ieindling. J. T., t Ltta uer. S. B. and de Oliveira. T. J. (1970): Mean action

time 0/ the X control chart with warning limits. Journal af Qual ity Techno-

logy, Vol. 2, No.2, pp. 79·85.

30. Williams, J. M., and Weiler, H. (1964) : Further charts lor the means of trunc a-

ted norm a l bivariate distributions. Australian Journal af·Statistics. Val. 6,

No.3, pp. 117·129.

C. Computers, Aut oma tion . and Quality Control.

31. ArJ/otd, \II. 1:. (/')(,'i) : Qllality control and digital control Computer, Annual

Techn. ConI. Trans., 1965 ASQC, Los Angeles, Ca., May 3·5, p p , 329·3.40.

32. tl ac ks ie iu, g, rnt d Baller, A. (1973) : Quality control o/mal/u/acturing proces-

ses ui tb t b e air! 0/ process ca lc u la tors (German), Qualitatund. Zuverlossig·

keit, Vol. 18, No.5, p. 117.

33. ll arr ts on, 'Ib, V. (1965) : Crnn put er ap pl ic a tiou s ill quality control operatiolls,

RSQC ConI. Trans., Rochester Sect. ASQC, March, 1965, pp. 23·44.

34. Huggins. P. (/954): Statistical c om p u ter s as applied to urdu s tr ia l control, Jo-

urnal of 'he British Institution of Radio Engineers, Vol. 14, No.7, pp.303.321.

35. Ka lle t, I:. T. (1965) : The com pnt er -s anotb er tool for quality control, Industrial

Quality Control, Vol. 22, No.2, pp. 89-90.

170

36. Knt s ura, K .. l ma iz nnr], ,II. a u d Nok am ura. S. (1965) : 1111 ap pl ic at ion 0/ c o nt lnt n:»

/01' pro ce s s cou tro] ill s te e l iudu s trv, Rep. Stat. Ap p l , Res. JUSE, Val. 12 ,

No.2, pp. 21-36.

37_ Kre/,,,,!a, J. and Ul lric b, M. (1964) .. Sialislira! C<JIIlru!o] prodnctim, uJlldiliol/s

[rom tbe s ta u dp o in] 0/ ant om at i o n (6'erlll({II). Wissenschaftliche Zeitschrift ,

Vol. 8, No. 3-4, pp. 269-275.

38. lreherma n, G. J, (/965) : Sialislira! process c outro! am! 1/1,· illl/I(/("1 0/ au tr, .

mat i c process control, Technometrics, Val. 7, pp. 283-292.

39. Vim Osinski. R. (1966): COmPIiI/!/'s an d yom job. Quality Assurance, Vol. 5.

No.3, pp. 20·25 .

40. Savitzky, A. (1966): Co iu put er s r e du ce d at a /01' b e tt e r lIIJaIiI)' c on trol , Chern i.

col Engineering, 101.73, No.5, pp. 97·104.

41. Whileman, I. R. (/965): Qlla!ilv corrtro l ant! t be c om puter, Annual Techn. ConI.

Trans. 1965 ASQC, Los Angeles, Co., May 3.5, pp. 619-625 .

42. )'ales. F. (1966): ('ollljJlllers. tb e s e c ou d reiolnt ion ill s tatis t ic s . Biometrirs,

Vol. 22, No.2, pp. 233-25l.

43. Zotndoua, A, N., Rv z nv. Z ({lid t'Llric l», ,II (1968): A s urnev O/SUII/(' ref «u t

Cae cbos t ocak uor]e in ant om a t ic s ta t is t ic a l proc e s s cont ro l, Journal of App-

lied Probability, Vol. 5, No.1, pp. 43-54.

E, l s oton ic . Re pre ss iou Proh le m.

44. Bnrloto , R. E. an d B1'lI1Ik. II. D. (1972) : Tb e is oton i c repression prob le m an d

it s dn al, J. Arn er , Statist. Assoc., Vol. 67, No. 337, pp. 140·147.

45. Barl ou, R. Eo, Burtbol omeu-, D . .T., Bren.ne r, D. J. au d Brunh, II. D. (1')72)

Stalistical tnfereuc e uu der Order Re s tric t ions , John Wiley and Sons. Inc. ,

New York.

Centro de Estadistic a ,\!alcmalicaAcademia de Cie nc ia s de Rnm an inHI/carest, Rumania

(R ec il? ido en ene 1'0 ele J 975)

L i L