120 Designing capable assembly stacks

l iorn the Conlbrmabi l i ty \4ap brsed on the FMLA Sclcr i tv Rat ing (S):

f , / , . , : . l1 r

r . i l " l I ( i l " ) / , 1r re)

f igure 3

Erch 1(

suPPlr.

physlci

1i: b i la lcral to lef lncc lbr i lh conrponenl char|cterrs l rc

/., : bil tcr.Ll tolerrncc li)r assembly

. / r , . - componeDt manuftrct l r f ing v.rr iabi l i ty r isk l i ) r i1h chrnrclcr isLic

a rr , : requircd process crpabi l i ly lbr Lhc asscrnbly lo lcr lncc (shi f ted)

A l low chl f t l iJr lhe lo lcf tncc s l r rok mcthodolog) ( .1/ 'R, '1 lo/ is thown in I igurc 1.5.

I , l lcnrcnls ol l -MtA. CA. pfoccss sclect ion nrclhodology. lsscnrhl) scquc|cc dir l

gfrns ( lhrough D|A lcchniqucs or (A).rnd. ol co r \c, i rdcqtr t r lc lo lcf l rncc s l t rck

nnxlc ls. s ln)uld bc uset l in or i ier lo l rovr( lc I conrplc lc sol t r l1{ ' r lo thc rsscnrblv

sLnck problcnr Addi l ionr l ly . ln n( lcrs l r rndiDg ol gconrclnc lo ler .nc 'ng. f r )ccsscrprbi l i ty in( l iccs Ind sclcct ion ol kcy ch|hcicr ist ics is uscl i r l ( l -crncr ' l996tr)

ln i l i r i l ly . i1 is tcconrmcDdcd thl l r i l l i rssclnhly scqucncc lbr the lo lcrrncc \ l r rck ( lcsisn

be dcvclopc( l .nd th i rL uDy custorncf speci l icr l roDs bc nolcd, l r "p icr l l ) r lhc l iD! l rsstnrblv

t() le11rrcc. polcni i t l l lu i lurc rno( ic(s) l lnd thc l :Ml lA Scvcr i l ) ' I t r r t i l lg (5) ( ) '1ce r i r )

lsscDbly lo lc ncc hI |s hctn lssigncd Lrnd lhc lcvcl o l crprbi l i l ) dclcrnrnrcd l ionr lhc(inli)nrnbiliiy MrLp. dcsign lolcrrnces lin ctrch eonrpolcrrt in thc slxck ctrl bc

rssigncd. Thrse rc thcD op{ilni/cd bcrweer rtcccplnblc fisk vlltrcs inili llv, which rrru

in lhc crp!blc rcgion ofrhe pn)ccss (r tnd t rcccptnblc pr 'odtrct ion cost) b) ' runningn

{rnple rol l l inc Ol coursc, lhc use ofcompulcrs in lh is rcspcct grcxt lv specds up thc

t i lnc for l l solut ioni howclcr . r prrpc| 'bnscd rnulysis is r ' l ! ) possible Lrs showD lr ter '

Ifthe lsscnrbly tolerrncc ctn ol bc nrct by optimiTrrlron. lhen mLrrc crtptrblc processes

will need to bc investig.ttcd bl lhc dcsigner' These ctrndid.Lre processcs coulcl be rr

sccond ry- opclitlon fot incrcased rrccuracy. for extrnrflc lurDingrboring lall(,wcd bv

c)rlindricill grinding. or n completcly dilltrent pfoccss brscd on som0 lcch icll.

cconomic of business rcquircnlenl I hc imlortance ol hrrving rdeqnare mnnulrclurlng

k owledgc rnd componcDl costing processes is lunhcr cnphNsized.

l fopl in i rat ion is chieled using the plocesscs choscn. then ihe sL ndard devial ion

esrinr.,ilcd for each conponeDt tolcrance ctn bc conprred lo lhc rcquired rslcmbll-

s l rnd.Lrd devial io l r to see i l o lcrr l l cap bi l i ty on lhe rssembly lo lerance has bccn

achic lcd. l lexcessivc v.rr i rb i l i ty is est imated t t th is stage on onc or i$o chrfaclcns

iics. thcn redesigD will need 1o bc performed. Cuidance for redcsigD can be simplilicd

by using rdrrrrnt) arrlfr/:t. uscd Io estinrnrc lhe percentugc conlribution ol thc

variaDce of each conrponenl tolcrance 1o thc .tssembly varirDcc. where the \'alance

cqLrals or. I t inbws thr l l iom equat ion : l . l l

3.5 Application issues

*( i )* *(3)\q/ \d i . /' : (1) (1 l r r)

Application issues 121

Figure 3.5 Eemenlrol the C4PMroi methodo ogy (adrpted {rom t€e and Woo, 1990)

|:.Ich lern when mulliplied by 100 gives the pcrc€nrrge contributior ofeach compon,cnt sv.rr i rncc. 1,2.. . . , , l , rom this .rnd other inlbfmlt ion in t ,areroch f t form ( iuchr! the stand,trd deviarion mulliplier, :). rhe designcr can quickly foc s on the problemcomponenls rn terms ol ddninanr lafialion. lack of crpubitity. nccd for SpC orsupplrer dialogue As.t design evalurr ion package. CApRAt.t js rble to qujcklyassess whcthcr a desigD is going to bc crpablc. and if nol what conrpdrents rccluirercdesignrng.

In addit lon 10 understanding the stal is l ioal io ler{ncc srack models and the FMEAproccss jn developing r proccss crpable solurion. rhe dcsigner should aiso addfess rhijphysic.rl assembly {spccrs ofthc rolcfance srack problenr Any addiliomli.aiture costsdetermincd using CA ll|e indepcndenr of rlhcrher thc rcteranccs nssigned ro iheasse bly st.rck ,uc capable or noi. As prcsented in Chprer 2. rhe e)mponenl

122 Designing (apable assembly stacks

Assembly V.Lrirbilitr- Risks Analysis is key lo better nnderstanding the effects ol rconponent s rssembly situali(nr on vari:rbility b,v quantiiying the risks that vrriousassembly operaliors iDhcrcntly cxhibit. By identifying componenrs $ith high assem'bly risks and potcnlially high lhilur€ costs. further design etrort is highlighted rndperform€d in ordcr 1(] idcntily rhe associrled tolerrnces iof the conponent s optimrli i l t lnd lnncr ion.

3.6 Case study - revislting the solenoid designA { ir f l i l i c.rse study is presenlcd ncxt 1(r i l lustra(c thc usc ol thc kcy clcncnts of lhc4.,1PR,4kl nrelhodobgy. | igurc 1.6 sholvs thc 1(r lcrLncc s(.Lct on thc solcnoid cndrsscrDblr- dcsign as firsl cncountcrcd in ('hrptcr 2. Thc kcy rcqurrcnrcnt w.rs lhatthe plunger displrccnrcnl. lionl lhc sealing f.rce through the soleuoid ktefrncesl.rck 1o the plungcr cnd sc.r l . musl be wi lhin a toler i rnce of i0:mm. otheNisetirel fiow rcslriction could occuf. 'fhe prodLrll wjll bc in lhc \ir'.l flnl! rctu l c tljgorlrs iL hrs l i l t lc c l l tc l on uscr srfc ly i f i t f r i ls in scrvi0o. which rcl t l tcs lo t ln IrM I IA Sc,rcr.i l r - l t r l ing ( .s) - 5

Il

5

,l

(a) 8 mm

f':| ----l [:]-I t---d]<

< @o 2..

Requir.d plung.r dlsplacsment = 0.8 1 0.2 mm

rdvrntag

ol lz |nnr

3.6.1 P

' Ihrs cDLr

Manulac

fin 'tol

Simi lar l !

risks. ThTlre tir

n1ultiplle

'The6 mm end seal dimension will be used in the analysis, nol28 mm

figure 3.6 50enod end a5semblyd€5lgn

6l tz., aSSEMBLY STACK

-- ' iz)r "-| f izz..

Case study - revisiting the sotenoid design 123

Trbl€ 3.1 Resulls tablc lor a papcr brst .natysi! ot rbc solenord asehbly sta.t desisn

r'(nrntir:! Tolc nce varirnc!t t r : , ' 2t cun| hdtun l i i r (onrr ihurtr i r i )

la r i ) . 100 td .1r l0t l

l . :t )Il . lII

I)l

I0250

1.850011.78

t7 00021.7 0 060

I 7 0001t.? 0 0t9

As\.rbly oflrNr /. = a0$inm/\*flnhrJ" nrjrdrnl d.r{LnD. d 00elimA5\.mbr dr u. a,rr : , , ,11, i . l l ]e

Thc sol€noid dcsign will fi$t bc rn.rlysed in n .papcr-b sed. .rppforch. fo owod bydcnn,lstrah(,n of thc rcsulls fronr lhe (,4pR,{/r,i sotiwarc p;ckagc' which rrrkei

{dlanlage of thc compurcr coded algol. i thms ro 6nd r ln oprimi/cd solut ion. tncludedrs parl ol the problenr this t in le is thc dimensi(nlal character is l ic on thc t .ucl port blockof l2mDr. or iginLr l ly s€t by a suppt icr.

3.6.1 Paper.based analysis

This entai ls r lssigning dcsign $lcf trnces tbr cnch chriructcr is l ic in lhc l lssemblv stLtokhssl on lh,^c Fr\en h) rhe nr(\(c\ , ( : r t rhi t \ mrn, I

^ntcn, i r \ IV,. hul in i t r \ t rr

thc ellecls ol processing the nnrcrial llnd gcomelry ol each rhrough the (i)nrponcDiManufrcturing Variability Risk Anrlysis.4,,,. Tbe rcnder is rci.efted r(, Chrprc;2 for adct i led expl: tn t ion ol rhis prrt ol rhe ani lysis. Forcxrmplc. rhedimcnsionot I2nrnlfor ch rncierisric number l. w€ cnn rctar ro lhc turninglboring Drap (Figure 1.2) andlocare d blerancc rhrt givcs I r isk on the l i rnirs of tcasibi i i ry. t . . . i : r . t . f t i ,lolerunce is +0.007mm from the rn,tp. lncluding ihc cfecis ot proccssinq mitd.Lcel . hou.rer r / , r 1.2r. rhr . incr( . r ,c, rh i Jcngn l , , tcr lnc( lo -rr , tnrn; th(f inal ' to lcrance al located would be +0.0tn1m to sive,1 :1.7 rnd therclbre4.: 1.7. becausc no account of thc surface roughncss to process rjsk is nrade.Similarly. for the other 6vc characieristic dimcnlions jn the a.sscmbly srack we canallocate a dcsign lolcrance ftunn the respective m ps and nmrlysis ofits variabiliryr isks. ' Ih is is sunmarircd in Trbtc 3.1.

Thc linal asscmbly blcrance. /r. is the sralistical suln ofrbc compoDcnt toicrances./', and can be dcrived frorn equarior 1.2 duc ro the lict rhal the standard devi.rtionmultipliers, :,. fof each (terance arc th

i r i <, i (3.2r )

'The a7 PR,.l7,/ demonstrulion solxrarc is rvaitahie lion, tr,c ruurors.n requcs

124 Designing (apable assembly sta(ks

f6)

Characlensl c number

t igur€ 3.7 Pareto.hdd5hownqlokGncecontbl to io l€a.h.hdra. ternt lothelna astembytoeran(e(lor tlre paper based analynt

' l h is cqunt ion r l lo l ls us lo dclcfminc c.rch !omPoncrr l lo lerrncc s conlr ib Lion 1o l l re

l inr l t |sscnrbly lo lcruncc by usiDg l s imi l t r r r lnrotrch lo lh l r prc\cnrcd l i r r scnsi l iv i l r -

r r lys is. l t in lows l r ) rn cqtrrr l ioD l l l :

{r . l r l

Al lhough Lrn cs( i l f i r tc l i r f thc c lp lb i l iLy ol lhc t rsscmbly ( ie lcrnincd l ronr equl t i { )n I 7

ls ldcqul tcr l ( r r l .19 l ; r Nrr I :MI iA Sclcf i lv Rnt ing ( .51 '5. lhcl ior l i rssonrbl)

tolcfLtncc is 10..108 nD\, grculcr thtrn thc ltrrgcl oj l 0 2 l]]ru A I'rrfct() chrtfl show"lg

the rcsul ts ol thc (olcrrrcc sonsr iv i ly r tDI lysls is showD ir l l r igLrfc I l . I1 i l r ( i ic t t lcs lhxr

componcnt chir ctcf is l ie\ ; l rnd 2 hxvc lhe grcr lcsr corr l f ibul ion l tcdcsigD cl l i ' l

would then l i )cus on thcsc rwo chnucter is l ics Lo rcdt lce thcir ovcrtr l l t ( ) lcrnnce conl '

bul ion. rs wns concludcd i r r thc Borsl cusc n. t lvs is in Ch plcr I

Addi l (nrnl ly. wc crn delcnl inc tbc \nr i r r rce contdbut idr o l cach componcnr

roler ncc 1{) ihe l inLr l lsser)rbly t (ncfrncc usiDg sensi t iv i t r" anr lvsis. thc cof fespondrDg

ch.rr t showD in r igurc LI t . A nominr l i r i rgct ! . t lue is indic.r lcd t t t 100' f ; i ' r . \ !here ) t 's

thc numbcr of componcnis in thc strck l - igure I i l shows this in I ' fc lo chr( l i )nn

agrir. tlnd fcrches thc s.rme coDclusions abole. rs expcclccl

on thc gerefrlr(m of a fcdesign. sinilar pfoccdure would bc used 'rs thrt

describcd rbolc lo iterdlc a process criprble solutioD whefe lhc lrrget tolcfnnce oi

+0.2nr l r l rnd.Ln overr l l r '0r : 1 3: l are.rchicvcd. Howclcr. the process 's

speeded

up grcally lhfoLrgh the usc of sdiw.Lre incorporaling the proccdures rnd knoNledge

3.5.2 CAPRAI'I soflware analysis

The dimcnsions ol cach component in Lhe ioler0nlc slack design (Figure 3 O. rheir

respcclile malcrials and manlrfllclur g proccsscs are inpullcd in sequcnce rnlo

a,.1PR,.1trl. Also rcquired arc the trrgcl assembly Lderance and llre f MEA Scverrt)

30

2A

10

Figure :

l {n( in!

which

' ( l i) (11) ,(;1)

Irigul

!hc l i r

I1 i l

for a

snaLl

\\,hicl

f/.)

(:1.t r )

rt,

f igufc 39 shows lhc resnlts ol rhc ofr inr j / t ion fout i re for rhe tolcrnnces Forcapabi l i ty at this l i rst lcvel to bc rc l ized. r l t tbe conporenl r isks rrLrsr bc bebwlhe l inc on conrplct ion of tbe opl imizl t ion rourxre. rnd subsccl l rcnt ly thc ci lprbi l i ryrequircd wi ih tbis dcsigrr conl lgLrrr t ion crnnol be Nchicved.

I t rs cv cnt f roor Figufe 1.9 thr l rwo out Lhc six componenti churacter isr ics rrepfevenl'ng optimizalidr ( ! was dcrcrnined iD rhe papcr brsed anrlysis). ,tnd lhere_li)fc fedesign cllofi herc is required. spccilicaltl rhe basc lotcrance ol the sotcnoidbody and rhc pde thickncss which ,rrc borh nnpact exlruded. A ta.rture ot. rhedcsign related b these two rolerances is rhe bobbjn dimcrsion.rl rolcrance. whichscls the position of the polij liom the v)lcnojd brsc turrhcr redesign d ta is showDon the f inal a, ,1PR.4/r/ screeD in Figure t .10. Redcsign drra iDcludes a basic esr inalelbr Cnr. and an .rssembly tdcrance calculalcd from !he proccss capabilily maps thalwould bc chievablc lbr the givcn desjgn p,tfameters.

A rcdcsign solnLion of the blcrlrnce srack i! shown in Figurc t.n. Ir nrlolves .tsmall desigD alteralioD (circled) rvhich eliminalcs the pl.rstic bobbin from thc toter_ance srack by machiDing a shoulder on thc inside ol the solcDoid bodr,. up bwhich thc pole piece is pfecisely located tso. second f\, rnachining proccssei are

Case study - revirhing the rolenoid derign , l \

/f ll\/t

: b i l ! lc l r l f f imcr l r ) lc f nce t i ) r i th cornp{)nenr chirrnclelsrrc

: bil tcfrl tolcrlircc liJr usscDbly

- nLrmber ol componenl rolcfrnces in the rsscnbly s l rck

50

30

20

10

Characteristic number

Figurel .8Pdreto.hadshown!varan.econtrbl torofed.hchacclerst . torhefn,rass€mby!aranc€(tor the pap€rba5ed ana yst

lkt ins ( . t ) to gi !c thc lnfgcl ( ; , . Thc prognrm iDir ia r o l l lcut l rcs l pdnrcf to lcnrncc, / l '(1hc s l l l is t ic l l su|n ol lhe pr inrcr lo ler l rnccs cqul ts rhc sscnrbty lo lcmncc. / , , ) ud . r f l ( ;c l lcs lhrs kr cach diDlcnsi(nr Thc pr imcr lo lef l rnccs l rc c l tcut rcd usiDg cqurrnD ] .11,whlch is def i rcd l ionr equ r jon 1.11, Ihcy rrc uscd to nlr lhc opr iur i / t i (u rour incrr( l thcir Icspccl i !c I isk vr lu$ l fc cr tcul lcd UoDr lhc proccss crprhi l i l r nrrps:: : ]

' i l , r t

126 Derigning capable assembly stacks

: , . : : : : : : : : . , : . . : , : , , . , . . . : i t : . . : : : : : . : : . . : : t : : : : : : . : t : . . . ., : : : t : : , ' , r i ] : : . t , . . t i : : : t i l : l i ; i i i i r { t ; , : :at . td i ] i : :h,

Figute 3 9 t l i r l lw,r t l l i l ( , r ) .1) fLo.nr! f \ ( rnnolr . . r r ln/rdl , r { ) l ro( l lof inr . r r ( tdf i ( t r l

( l r i r ( l , 'ur ( ) r r 1hc f ( ' r l r1)() l lorrs $r l l r l l j . lcrs ll . ( ) / \s l l r ( f f $( fc InxchIIr ! o| ! r r l io i rs () I

cr)rDp(! icnl c,^ l Incfcr \ r $rs s r t l l I r t r r l l l r !. , rh l t \ . .11,r f q r l ' r l . . l r I - ' r , . r r . . . , I .

IrlVa ues ol loerance rsk A'Lnd care rhal optmizato. is

chataclerstics dom nal ng

I I

Figure l

1tr l l l l i f1 l

I igurr lI t rs. ,

i \ l ikc l r

\\'ith (crp:rbi l iAlAnl I Pd.r l.

.i+;-ni..!: :. ::i,!ii-i.r-!. ]t@F}

ro liffi lstatus * "ltri"\

$;I

.xfxbr l i l ! rs ( lctcrrr1inc( l l ro l r 1: igurcrh.sc r \ ! ( ) ( 'or I t ) , ,ncI ls rr)$x! . lhc

1l 'c ( lc iq. pr l rnrc l (* in l t ) ( 11'R, l to l\yc i i r r l thc hfgc:r lo l f r rn((s l ( ) r 1h.

,"1

tX

Figure l -10 Ffa a/Pn4blsrreen forthe soenod toeran,:€ n,r .k dosqn

Case study - revisiling the solenoid design

ASSEIIIIBLY STACK

6)z: mm

@o.z mm

121

@zo mm OESIGN

L

I

F

R.qulr.d plu.ger dl.phc.n.nr -

0.8 r 0.2 dm

'Tho 6 mm 6nd soa dnonsion willbe used . the analyss nol28 mm

Figure 3.11 So€nod end aslembly redesgi

lc.rst r isk arc opt imized io Denr cclunl v:r lue rs shown in t : igure Lt: . Thc f isk v luesdeiermined nt this sl ge rre \ ,ery low. closc to Unity in hcr, . ind th€ si tual ion tooks

Figure l . l l shows the cl lecis ofdre marcr i . t l f rucessirg l l t ld gconrerry r isks t i ' r c chcomponent l rom thc component |nrnul.Lctur iDg vurirbi l i ry r i \k.4Dj. rnd lhcs0 archken rnlo considcfrtion 1ll the cllcul.rlioD ol the 6n.rl cslnnrrcs tor ( rk rnd CF tiJf

Prrt ol thc dcsign inlofrn.Ition providcd by rhc softrrre is rhc sl nd fd clevi.rrion

'nul l ip l i€r, : . for each component tolemnce shown rn Figure l . l4 in parero chrr l

li)nn. Additionally. sensilivi!y aDalysis is used lo prolide a percenhgc conrriburionol e ch lolcrlxlce variance to thc liDrl Nsernbly lolcrance \ariance as shown irFigurc 1.15.

Il is cvident rhar characterisUc nulnber 5 has rhe largcs! contribuiion (89.8%) and nis likcly thrt ifrhis is sbiitcd. thcn the final rssembly distriburion wilt bc ihifted from

'rs 1 rgcl vrlue, suggesling n nccd lbf Sl,C in produclion. Horve\,cr. rhis redesign

solurion is lcfy cnpable (as sbown in the limrl al,lPR,4/o/ screen in Figurc 3.16)wirh Cnk::1.67. which theoreticaliy rclalcs 1o no failurcs. The acrual pfoccsscapabiliry of the asscmbll tolerance will, in lacl. lie somewhcrc beiween rhe rwolalues calculated for apk and aln, bxt using thc lbrmer \\,e arc considering thepossibilit]'. of shili thfoughout its life-c"v'.clc.

)-,*-a:

128 Designing capable ass€mbly sta(ks

tigure 3,12 Chai( showing optimized toerances lortol€noid tolerance stack redesgn t igure 3.14

Thc i iD:

which. i l

Componsnt man!tscturngvanabillly rsk, q6 and Cok,

figur€ 3.13 Data screen for soenoid tol€ranc€ stack redesqn rigur€ 3.1:

case nudy - revisiting the sotenoid design 129

Figure I 14 l lnr . i , , t r i t t r r l dov r . r nr | lLt f , ! l

' lhc l i j r r i lo l . i rnf(s lhc ( lc!gIcr \ i )ut( l r l tocxlc lo l t rc .onrtr) I ( . r ( t i I r . r )s ioIs l f (i r l \ ( , sh(\ !n I r I r rUr( I l6 th. lotLJl Iec \ r lucs i Ic !L!cr l , ) lhr( . . ( tcernrxl I t lc(swhi(h. i l f ( ( luIc( l lar t ! i r r r i ( . i r t usc. ! i I r l )c f ( , I ( lc{ t o1] $rrh I I IL j r r i r t c j l i . . t io 1tr .( i \crr l l i rs\ ,nrhl t l t ) l . f rn. . . l i ) f c\r r rJr tc t 0 t { ) t I In t ( ) l r t ( )0I n

Nomln.lt!rg.t. 2O"O o/o

Figure 3. l5 ahaft s l rornq !aran.€.of t /h l ton ofearh lo lerrn.e lo t re i na ar jembrjrran.e

130 Designing capable assembly stacks

l r ,hre8o4t6dFo id

[-'" ""p"ir" r"r.*"""allocated Io the dimensions

Figure3. l5 tnd (APRArolroean for soenod iohcnco nr{k red€5qn

:t9:r the applcll

u iLh the grerrnclu{ l ing th

Thc in d!thc str t in ic,designcrs. Ilhe crprbi l i l

l -hc \ors

. Sinrplc to

. Li t t lc iu l i

Thc str t is l i !

. Morc di l l

. C n inclu

Cdnprr ing r

A conrpal'trli\'c wor\( cusc lsser)1hly rolcI1rnce brscd on lhesc cupnbtc totefunccsopt in i , ,cd using thc st l l is l ic l ptrorch is sho$n rs .0106urm iD lhc towef tc l ihrDdcofncrofFigLrc:1.16.whichisgrerrcr lh ntherrrgcrol +0.2 |nnr. A thol oughrnr l ls is ol thc redesign brscd on rhe worn casc rnodel w.rs prcsenred in ( .h pler 2.Howeler, lhc ssumption lhrr cnch conrponeDL dnncnsioo rus l l i ts mr\ inrunr ofminjn or hni t wrs c le r l r - noL lhc cuse lod rhc lcvel of vrr iLrbi l i ty expcf icnccddi l lered thfoLrghoul the courponcDls in the assenrbty st ck. In pfuct ice. lhc wofstc lse apprcrch gi les l i t le indical ion of the impacl of rhc component lo lc l rncedisrr ibut ions on the f in.r l . rsscnrblr- lo lefrncc disrr ibut ion. Lc v ing out rhis datacrn hrve.rs grc l n imprcl as lc v ing out thc L(ncfnnces in rhc l i |s t phcc ( ofp.1993).

Thc inadequacy ol thc wofst crse nodcl is evidert aDd lhc st l t ist icr t Dalufe ofthcblernncc sttlck is nrorc rcalistic. especirlly wh€n inclrdirg the efltcls ot shifteddisl but iolrs. This bas lso been the conclusion ofsome ol rhe l t rerarurc discussinglolcr ncc stnck models (Chasc t lnd l ,arkiny)n. l99l i Hrrfr- nnd Srewarl . 1988: Wuf/ ll/.. 1988). Shifring,rnd drifling of componenr distribulions has bccn s id to berhc ctiel ferson for thc rppar€nr disenchantment wilh stniisrical rolcrancxrg inmanulactunng (Evrns. 1975). Modern cquipnrert is licctuenily corrposed ofthousands ol componenis. all ol which interrcr wilhin vrrious rderances. Faituresofren arise frorn a combinaiion ol drilt condirions r.trher th.rn rhc tniture ofa spccilicconponenr. Thcsc are more dilicLrll ro predict rnd.Lre ihereforc lcss tikely to bcloreseen by thc dcl igner (Smith. 1993).

o+lX

Summary t3T

. As\umer rolcr. lnce di i l r ibuf ion on mrr inrum,lr mrntmum l lmir. L ( .rnt , , rm.rrx\n gcnerrreJ for reJc( ign turr \ \s(\. i"..r,Jllj;,:;1,:"r"","rd.

terdin! ro unn((c_tlrirr ristrr r,rerlncc{ nd. rhcre,r,rc.

Thc slaristicul' tolemnce strck approach is cndraclclrcd by:. M^.)re

-Jinj(ulr m rhernJf i ,J l l ) tL(,nrpul(r ncce,sirry ). Assun)cs t( , tefJnccs l t re rrnd,,m ! i rr i btc\

: yp,:,:: j :t:, j : l l l l :rplrrni,:rrro,r of rorcran..c. rn rhe ,\c(mhry. \ rn nef l , , rm \enjr i \ i r \ rnr ly, i . r , , r r(Je\rgn nurto,r . \. (nn inclULle cf le , , t , l i t t rnF ind ( lnt l ing ofcompnnenl r , , lerrncc,. \4or(.rei l tst i ( r tpre,enrrr jon ot actual . rrur,rr<,n.

h) thc fn l tor jn! l. Simple k) pcrform

H:,Jii:':":iil:f,'i:"::;,:i,i::::i:ii-r*r".ds.wrrh inlcsrated n,anur,,cturinsi:lli:i,::: lTlSl:::, r .",ry rr. i,,".,-i,,";;,;';t, ;::t; ::,iii:,il::ill:il:.lill,iil,ii:ll,::::li:i-c,..."i'.i, .,".k.,. .;;;;,;;'iJlitil;.iji,i.i.,l.l.il;csscnri,tl way o'idcntjryi"e,r," *p"tiruy

"ia""ig,,, ;;jffi"il il?,i]::J;l;li