&I

rI

0uai i ty, processes and contfot 21

SPC includcs .r ict of tools for managint Pr.o.csses, .nd detcnnining.nd monitorhg thc qLral i tv oi the output of an organiz, l t ion. l i is alsoa straiery lor reducnlg variation in products, drli!eries, proccsscs,materitrls, attitu.lcs and equipment. Thc quGiion ('hich n.'cds k) heasked continually is 'Could we do thc job bcttcr?'SPC.'xists bc(rusc tlrere is, an(t $,i11 .rls.rys be, \'nriation in thc .h.racttristics of nrnterinls, .rrticlcs, scr!iccs, pcople. V.rriatr( has to beonclcrsinr.l nnd assessed in ordi'r to bc mana$ed.lht fe rrc soni{ b.sic SPC tools. fhc'sc a(: prccess f lo i \ r .hir t i fg(what is doft , ) ; fh(ck sheets/tal l t - charts (h(N often i t is. lone);histograms (pictures of v.rr iatn)n) j gnrphs lprtures of \ ' . r r inr ion wirht inrLr; I ' . rct( ' rn. lysis (pr ior i t iz inB); cnusc.nd efteci annlvsis (whntci , . rso thf plr)bl fms), sci t t . . r di t r , j ms ( xplor ing rcLrt lonshifs); contr( ' l .h.r ts (nl)ni tor ing vnr intnJn o\1r t inre). An r lndcfstrnLl lng of thct(r ts rnd hr ls r{) usc thcnr r( ! ! i ( s fo fr i , ) f knowlfdgc of srr l is i ics.

References and furlher teadingI ) , , . r lnF,W.l l . ( l t )81))(rr l i , / r / , , ( r r !^ , \411,( . r j l l rn l r f N4,\ , LJSA.J),rninF,WL.( l t ) ( ) . r ) r r , Nfr r r , r r {a, , NJl l , ( . rnrhrnlr !Nl4. USAIirgcnl) . ruoi , .^v (r , r ( ) r ) r r r r i Qrd r / ( r r r rn, / , : rRl t i l f , Ntr( i rJw t i r t j .( i , ) f ! in, l ) A ( le* i ) I , ldrrr i r lL Qr/ / r rv, In.e l , r '5s, N.w \1i .1, t r \ r l . rn ln.r ,M.nd(hni l t ! ,1.( t r r ( ) t )&. , , ! , r , , I r l1/1t( ' , \ ' t \ \nt i \ t A Nrr l i t t : t !

/ ,4 / r^, ! ' rs I . , t r l , i ' r , Ni . | l )1, ,s In. , ,L( ! , | (n11on, LrK.ls l , ik iwr, K (hirnsl , r r ( { by l ) , , rn l l l . , , l (L()r l5) l l r r l t ; l t ) t r lQtulr t t t . t t r ) l l

/r, /,,t,r[i hrrr/, h1lrln | | l.rlt, ljt].woo(t (.]iri5. Ner! vr k, I s,\l ( ) i ix ! lJ | ( l ( l ( ) r1) lo/r '1, ( - , . r tht t l t r t M.1r\rrr ' i i l / r . N& / j |5 ins, ( r4! ! r rs

, . r5, \4.( l r iw Hi l , N.w Yfk, US,\IUr.rd, lM. ( fd ) ( lee9) Qrdirr l / rn l l ' , !1, 5th lx ln, N1.( i , . r$- l l , l l , N.w Y( ' t ,

USA.(I)k l ind, l .S(2004)() . ,11.) f lonQrrr / r / Innr{rrrr , Inr t ( rw.{h, l l f incn[nn,

l ' f i .e, l (1q81) ^ i { r r

I tn Ti , r ' , cowcr, AlddshJt, UKshe$, l r r r t , i ! . r \ {1!3r). , ! r , , r CnDttulr l i ) l t i r r l ; t t rh\ l l ln r1,nt , V.n Nol t . r rd,

\fw Y(rk, USA (ASQ, l9r.l(r).shc\4rrrr, !!.A rnll Deemnrg, W rr. (19:19) statistid Nlxl!\| trn ttu Vna\Dnn

,'/ Qldiirl Cdrlrd/, Van N{,st,.nd, Ne\! \'ork, USr\.

xr 0iscussion queslions1 I thasbeenagued ihat thedef ini t ionof productqual i tyas' f i tnessfor

iftende(t purposc'is more likelv to lead to comncrcial sLrccess thanis a definition such as 'conformafce to speclfication'.

s,. , , i i l , r l r r r , , 1 , , r ) r , , r l , r r r) r , . ,Lr" I r ' i r j j l ' l r ( , r t L j r i , , r l l i , , \ ( , , r l ( . r r , i l r \L,( lL. l l l or i \ l , , f

lL rrLt , , r srr l r I . | , r r r I l , j ( . t I I f1, ( . r j tL,r l j r \ t .( . rL i . r r t \ t . I j r j , ) l h r : f \ \ r r ! rL! , , r t , r \11 LIrr i , r ( , r j r l t ! ., , . , l , j iLr . l l ! . t l ( \ r l t r !11 , r i ( l l j l l t I i, j : ( r ! \ l r j r : ! , r ( r i , r j t r j r l : j l ) l ) t i , , r l Lr I t , r , r ! r \ ( .

\ l i \ l ( ) t i \ \ t )L Il i ' ( . )L , r i l \ \ l , l r . r . . i ,r r , r | i \ t , j , r l r n l r l ) r r L l , r\ t l i l l ( I r j r i r i r r r / t r .l i ( t , \ \ . t t l ! . r , r \ l , r ( . t , , j r \ ( tL j . r r l \ ( t r , l . . t , r

r \ t , r i r r r t r . 1, lL j \ ' I , ,1.rr l jL ( l i l , . r ( . . ( ( I \ . I \ \ ( ! . I I , I , j I I r \ , , ( t ( , . r i t I , j I r ( t ) r l ( j i r j r r r rLLl , ) , tLr , \ , , , r iL\ l , , . .1. .

l l i , l , r ls , i , tLr , r l t . r .

l ' . .

t r .1| l , r r l l \ r Lr l , r l t )

lJ LoL\r

l i l ) r l t , , , I t r t r ' I r t l , , \ ( iL r i \ i rL\L t , , ( l j , , \ tLr I I I t , | | I i : I \ 1 I t I I : I , r II t , , ' , l . , r , ) \ t , I j \ ( ,1! I | , .1r \ l t ) / ( ! | t I I r ! l \ r l , t r r t , , l ) l r l ! | tL.r l .

t ( l , . r l r , \ , . r . \ tL i , r ( t* . . t r , r \1. \ ) ( ,nrr j | , r r j i t iL i r rL,1. , i l t l l l ( r , l , i rn | | L I I t , I L \ r . , r I I j I I \ t , L , Lt , r | | | j ( . I I I . . , j I r l t r .l ) i . . , r . . . . 11r( r . r t r . , . , . , . ( l l , \ t , , r t , t , \ t , I ( . I j i t , | . , | , L | ( , , | |\ t ) r , ( . , r I I j I I I , I I I j j ( I r I \ ( ! :L t , j j l r j , t r r \ ( . r \ \11 r . , !1t ( , . r+.r . i t iL, i . , ,L, l , ,L lL l l r t , t , l l , . r \ | s l \ t j ; l ! . r t t l r l , ) r . \ \ , f \ i r j r t ( . , [ ( .lLr . r l i ( \ lL1\ I I r ! l r \ . r r j : ( Lr f r t r r l i \ , lL) l ! r LLlr o I I I ( . j i I I I j , ! L)LI i I )LI I I I , I :L i ) l ( . r ,s t , . r ! L,r \ I i l , t \ I\ \ , , lL,r r i l ! , t , , i l rL.Nl . r j , r r t i r r1] t )Lr t r l , , r ( , I j , . L ( , I j j I r j | \ ( , , . I , I , L I I I j 1 I .I i !L rL r . lL i r : . t t ) \ \ l l r . : r t r , r t rL j r r , r n\ , |Lt $ t j , r l : t ( .1.s l j . r \ t !l i lL r l l j i r

' r t { (l , .L i1 i ,L

' f l ) l ( r j j t r lL t ) l . r ) t ! r \ ! , , , \ l r ) i f t r ( . i , r l t ( , r lLIL\ i , t , l

| ) | L t r t i , , I ) | I ' ' '

, r ( r '

I L , I I r , I I I I \ | , I r I r ' r rL. i l . r r r r l I I I , i 1 j \ I . I I I I 1 r LI \ ) l . r r . r , \ . .1|nr t , r Sl ' ( \ \ l r , j ( t , r ( . f t r , r l ( - . j (1r l t ) | i r r l j ( \ , . r j l r r r lL i l ) rL)1, r ' r " . , r , l l ! t i r l l ! . I , lL, l { \ .1 L, i! \ l r , r l , r ( l i . l ) , r : r ( lL\ i : i ) l ! l ) ( . r i ( l t ! ,Lr I r . , , , , , I ) | , L L L , r L I i ! I , I ( . . . .

t l rdcf5rdnLl rq lhe p 0re5sa&

41 ,

*

r References and funher readingHi ' l .gtof , l l . j . ( l !91) /n, 'n ' , ( r fn, , . ! r , r fn ' . . fu t / , \4c(, .w r l r l , \ f r ! \ i t rk,

L.CAl lJf tnrgn,. , l l . l . ( l r r95) / inr l l r l l r r . . ! rd, r \ ' l , rL l t , , r , r . \1.( ln,$, f l r l l . Nc$

V(r l . l l , N1 f ( l ( )Nl i l . ,1 r l r ' l i5 ' i , ! r r l . ( i r r l , r , ,srsr ,^, \1.( n)w Fl I ,N.r \ i rk,U5\

() . r f l , r i (1, l5 ( : i r l r l ) l i t r l (Jt t , tFt l rn"r l / r , r / / , r r , , lh lhr*ort l i I I lne i f r r ,

l \z(1. f , | ( l ( ) t )1r) l r r ' :1r t , t i t r , r , ' \ l t , f ' , ' / I / rd l r r rd l r ' , , \S( l l ' r \ r .N,1r sruL.. , ! \ j l , USA

*{r Discussion quesl ions| ( ) r l l i r t i | l l ' r i l rn ls l ( l )sr( i ( r ! ! ( { r l ( l l r lc I fst t ( ) i in, l ( fs l rn, l inJ lhen

l , ) inr f i \ | n pr( \c\s ,n \ !hr 'h ' r ( ) t r w( i r f .I ( , ,nsl fLr . i , i 's l . r t ( r r ( r l r l ' , , r nr i f { ,1 r l r ( \ \ 'ss () i \1\rr .h( , i . ( , $Ihlch

! , , , i In()h 's l l l .Nl i l .srr11 ! l , , , ! ( l (n l i lv l l r fLustdrr f r {s)nrr( l ( ,ut l t r l \ ,sLfp (1srn{ l n l ) r r ls , lx) ! ! , , ( , ! l ls icr l ( ) l lx ' \ ( ' i ( f , ,1 t lx (ust()rncr 'n,rLI h(rr f th. ' ! (J i . . (n i | l , l , ( ! r 'ss '

I l ) ( .s. f rh, . i f ( l .1r i l i l t l l \hni( i r ]e rn i l ( \ ! . l r . r r t i ' r i t t ( ) g l \ . r ' ( iynrnr i !n,r l . l o l , r f f ( ! r 'ss. l l \ f , r i f n l l lh. s\ ' r I t ) . ls Jr( l l ros t ln! . rn L, \c( lt ( ,gr l l r r f 1() . rNl , . r f i ( tur . ( i i i \ rn(s

I Wlr . , l r f r lh.st( , fs i r r ( ' i t lo l r \ rnrLnr l i ( in() l r fn!r \sn)r i r r r f r ( ) \ rr r f r i t l I l ( t r ! .h i f l lh s. in l { , I svslL . r i l ! . r f fntk l r .

. .1

&Process data c0 lecl on arr presental on 59 !

lnr l l is . r , K. (L.rs2) Cr/1, 1,) ( ) r r / r r r a,rr t . / . Ar i r j I ' r ( \h,Ll i r i t ' | \> i {n l lon,r j . ' I in! ] , l5 ( l (101) l l , r r i ! l r , r / r1! IJrrrr t rurrr , l i r i n (

' ! , ; , l rJ l : r ln,

lJr iLt .NLorL r- l l ( i r .nr .nn, (J^. ' l t , r ll \1.n, Nl ( l ( ) ! r ) \ / ' r d, / ln^rrr \ . / r , t , ! , r , r r r r / , l l S l ' r r Lr i l iLf \ , l l { \ lnnl

! Discussion quest ions( \ r t l i f f t lx t i r l r r i l ,e\ L, . l r l rJ r sVsl{rrr l r ( r l ) t i r t [ ( l ] 1, , t f {n.sslr i i t r ( i \ f r ) r . r r ts i l l rR\f f ! i t . t l i . I r i t r | ! r ) k 1 I i ( , I r r r ( I l r .s( . l r l i (n, i l

I ( ) l ! r r l ( ) rs or r r . r 'qr ' r rb \ I r r ' , r . l r , i \ in l l { l i i l i . rL l l r ( ,s$h.nni( ,u,r tn i : . . f ln)r i ( . ( !n l t r r .n l \ ( ! r l ( , , r l r int( \ l .LIL] l i h( , rn i l l r . (1, l r l (Lr lLn( i f ( l rk l ( , Lrr( l . i i1.{ l h)k\ i f l | l , l r tJ,r t r l . , r l rs, . r i ( ( . , ,1 | l )c5 i r ) i l i .l \ , , r f ( i , ( \ ( rs i / . ( l $ r \ ( r r ( ( ! i r t ( i r r , f lc , ( tJnrt t r r ! r i r i , ( . : \ , r . r t ) t ,Ls, ! r l ) . rn i i r r r , ( ( ! i r f ( ! r , f ls l ( ! r i ] l r l l r , r r l l r ' ( ( ,n( ,s l t r ( l i f l th(J( . .Jar S,\ t ! r f ( ( , f i l ( i f ( , f lc t r i l l r r r r t ) r l , l r , , i f ( l ! 'nr( ( i l r ' r l , \s l r \1, , . , r1

l ) ts i , t r i s inr l l l l . \ . r , rnshi(hlh t , ' r ' r .1()-(( ,Lr l i l h, . r \Lr( l l ( iu: .n t ' rL ld l , ' l { \ j r ( l ( . l r j l ( \ l f ( \ r ,n l r| 1, ,$ s ( i r l ( l \ tnr f r . r l , , ,s , ( ) l \Lr(h nt \ i f ( l \ '| | t^ \ \ \ r , , r ( l \ , , , r t .nr t , r , I lh. i r r l ( . f , . \ l , ,1 L| l ( ) t r . f , r r , , r : Lr l . . t ' in! \ r L l l

l ) ts( h, . ,s i l r ( . \ , rnr t (s. lh f r 'L | l \ l \ whi .h , n. , i \ , r i . ,1,1. l ( i r t ) r f\ . , r l i . r t in l ( i f r r , r l i , ! r h\ nr(rr i r i i i ( hrr is, l t , r f h\ . ( l i , iu, . r r rs, f l ,Lh, . L,rhl , .hr l , t r ! sh(^! : th( . , ( ! r ! f ( l ( \ l lh t | |n. \s. : ( ,1 : l ( \ 'L t l , jL( ,s rr)nrr , l l \ l l l ( f r 0 l l l .nr l ' l , , l . r l r \ t , , ( . ( \ l r js l , jL,rni)r I I I

' I ' | , j I ( , I I I i ( .

! : ! \ , . rnJ r , )n j jn, r l { jh lh( . , .s, , l l

Plale lhicknesses (cm)

, l

r!ri8t!r9l

: r ' l i

r39

292129rjg3004!03/2950312/2901300629972S1S

2943291t i29|i/28112981291829 t6301 l305829S6

300029ri529552907t9/ l290030r6302/29112S95

2935 301i l291i 30082959 211372986 2!563009 211853029 :03129t5 29322909 29492993 29i83014 2999

, .s l .b l ish . nr . fLr f , i . l r r ing spc. i l i fnt , )n l ( i f l . rb l f t r \c jghl , l

- , . t r fncf o j 2 l l l l Lrbletr t r . rs l , rkcn i foDr lhc p. i rdt |ct ion st ferr rnr l

II 60 Slat is i rcal Process Control

the $ei8ht of each tablei { as measurcd. Thc frequcncy distributionis shown belora'.State and explanr thc conclusions yo t{(,uld draw from this distribut ion, assunring the fol lowing:(a) the tablets came from one proc(ss?(b) the tablets came from two processes.

Measurcd weigftt ol tablels

Weighl(gm)

l{umber ollablets

238239240241242243244245246247248249.250.251252253254255

213322918212A2222t330ll0102

240

xlsz

xI

Slatrst ical Process Control

Discussion questionsDcsign . l.lass'oom 'experiencc', with the nid of computc'rs if ncces-sary, ror a team of senior n.rnitcrs who do not appc.rr t(, understifdthe concepis of ! ,ar i . r thn. E\plain how this wi l l hclp them underst.nd th need ior bettcr dc'cis(Drnirking procrsscs.(a) I r rp la i f i {hv nlmgi ' rs t . nd k) look. t in. t i ! , i ( tu.r lv.r lucs

- prrhaps

m(nrthlv rcsLr lLs, fn ih. ' r than obt.r in nn o\ ernl l p ictufc of dnia(b) Whi.h s imple technlqucs rvould yorr recomrn..nd t( , n]r l1agers iorimpro! i fg their un( i . ' rst . rnding of procrss.rnd thc \ nr i . r t i ( in them?(.) Whal is me.rnt by th( ' inhcrcnt v.rr iabi l i tv of a procrss?(b) Dis i ingLr ish bcir 'ccn comnron ()r r . rnd(, ln) i fL l spi 'c i . r l ( ) r.ssign.rbl i ' ) c.rosos of !Jf i r t i ( ! r , ind r ' \p ln in ho\\ , thr t fesoncc of spc.r , r l . , r - -nr . , \ l ! , ' . 1, ' 1, ' l l ' \ . r 'n l '1, lL. 1. , r i , t , . , . .'hr lhr ( 'xnmjnnt ion of prrcss di i . r , , r d ist inci i (n should bt madrLrct{ ' (en i . . r r rncy nnd prc. is lon l lxpl . r i r r fL| l l } ihc mrning of th issl i l ( ,nrcnl , i l lLrs(r . r t l rg r i th s inr fk r ! r , f ! , ( l . rv oxnrnpks, r lnr l sugg( 's i ingwhich tcchniqLros nr.rv t c hclpfr l .lk)r{ coLr ld thf o\ 'c l l r r r i rh i l i ty o i a p(rccss be Ll .h rnr inedi Whnt{ lo( ,s thc k nn ' . . rp.rbi l i l \ ' nrrn in lh is.( 'nt( xt?

3

I

1I

Chal

rtr 0b j l

5.1nI

| ( h. l t

"/le a n (

&Ige

xI

Slat is l ca Process Conlrol

Beferences and furlher leadingBesteLticld, D. (20001Qrn/ih/ a.rtr.l, 6th Edn, Preftl.e Ihll, Enillewood CliIIs

Nl, us^.Pyz.1.k, T. (1r)9f) l']v:d.rli Crid, ro SP(:, Vl. 1: rrr.irhnttal;,

Press, Nlileaukcc, !\il, l-SA.Shc$nr l , W (1931 5l l th Arniversir ! C'{rnnref t r r . r tL\ .

f(r,o,,i( (-,{trl rf Qrdtitn .,1 Mtirultl.tured rr\1rd, D.

ASOC Ouilih.

Itcissu. 19ij0)

wh.. lcr , l ) l r fJ Ch.nrbcrs. D.S ( l !9:) t i r r / r^ i r r r l i r t Srt isrnr, / iJr . f .ssC,rrrr l ,2nd F.dr, SI 'C I ' tuss, Kno\vi l l . , TN. U5^.

xr Discussion questions| ( l . r l . ! lnt( th( 'nr(nn,nl srr f ( l , r r l d. \ i i i i (nr o l thc nr. l t f l l , r , rnt( ,dr t . r

l ' .1(^! (g/ l0 or inLrres):

3.23530323332332l33363229

3330343l353.13.23.524353336

32343530343536303l

3t36

333.3343433323433363l3435

frc5U

.h,.

L' l

l l2 l3)

5t .6) .i ) .

r0) 4I l l i12) 1

Wo

323733

32

I l the.\ f ieci f icnt ion is 3.0 3.8 9/ l 0 nr inutcs, .onrmcnt on th( (dpdtr i l '

Dcsrr iLr( ihc . hn fnci . ' f ist ics of the nof lrnl dish- ib! i ion nnd constrLr(tnn ( ' \ . ,nrplc t{) show hou, thrse rn.ry be uscd in ansrvering qucst ionswhich .r is. l r (nn discLrssnns of specif icnt ion l i rni ts for a product.A boitlc r'illmt m.r.hnre is bcing used kJ iill 150 m1 hottl('s of a shampoo.Thc ichLrl bottLos \^'ill lx)ld 156nrl. Thc machino has bi'cn sct n) ciis-chirgc rn average of l52ml. It is known that th('nctu.l ;rnrounts .lis-chafgcd nnl(N .r normal (tistfibutn)n rvlth.l standard clcvintion of2rnl.(a) Wh.t proporihn oi the bottles o|erflo!v?(b) Thc ovcrllow of bottl.'s ctruses considerLlble problcms anc:t it has

iherci('c bccn suggcsted thnt the average discharge shordd bereduccd io l51nl. ln order to meet th \^'eights nnd me.rsuresrcguhtions, however, not morc than I nr 40 bottles, olr averagc,

tf

l ts

trat(,d n.packagir

agingpr

t r i i . , . r , i r i r r . l

r f r \ l ( ( r rL.r f . , . l l , . , r i I l ' , . i1 \1 11,( r , iJr l 'n1t l r l , i l t f r \ l r rL( i , ,1, , r \ ( , i ( t h\ L l t '1) , , ,1 ' (" .1\ l , l i , r , i ,1

- '

' ,1, , s i l l iu\ l 1( jL. , r ' , ,11 \ f f ( , r r l r \ \1, ' , , , ,1r i r l l ,L_(,1,1 -L r , r '

! . ,1t . l l ! ( t r rL , r l I i , i r r r l l i ( ! ) , t r r , r r rL l . \ t , j i , , l t l ) r r r i Lr ! ( \ l I | ' (

r i lL r r , r l i , ! , , ,1 ( l r , r i , . r l - 5rLt . t , , ,l roD: ! t , , , r r l | \ ( r l ' . ' r1, . \ , r l ' ) .1 L- l r , l\ l I r l l . ( l :

'1 l i l i i r r / r , , . i ,1 l l ,1/ i i / t , r , r 1 i\ lJr( i f i nt l , l l r . , \ ( r rL,$ ( t , r r r l )LL l ,a l L l iL \ ' \ . , , r r i . r i r ( j r i , ' r , ju , lL \ , \, ( , , r (1. , i , ! l 1, , \L \ ( rL! l l l , , i l l r ' \ , , l rLL_ st

, l i r r L r | ( i | , , ) I ) I I t . i I t , r , l t l l ,L \ r t , ( r r i r l , \ r ( r , , ! ( r l l rL i r i r i rL rr. l t ( , , ( , i l l i , . , l t - . 1 i . I l r l \ . r : rL l l l , , 1 j r , ,LtL, . r \ ( \ , ' rL l : l l , i l , , \ ,

j ( \ \ ( \ I , | ! \ \ . \ L | . r I r , L I rL I )L ! rL j l t , IL| , t ' ,L r ' j I , I i jL L| , I \ , IL \L, . . .

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- t , . t \ . , , \ \ . . t , . . t r . . \ . ..b( iu l : l l ) pcf . fnt ( i t \ ' ( iur proclu. l i \ .u l o i stc. i fn nl io .i \ r r t rc( 'd

'n ()rrr n, l rph(n(, co \ r rsnt i (D, I h i \ l r fxtnr. ieLj t |1In {)r l

f f ( !d: so|r . \ lJ . l i \ . r lu. ,s o,r . rppror imntet \ .ar l ) fo.cnt lots. As \ ! )L lcan s.r , lhf v i lLres df i , gcncr.r l lv ( , r thc high sido t r is \ i t r t rhr t i .ouhke urgent ic l ion n) r .du.c thc N1l I t so ih.rr m,| .n grr out t incsbn.k to corrrr t ( ,p. tnt ing sPefct .

2T

35

,1T

l r ! , r ' ! ! I I r ' | ! ! r (

MFR Values

&

\ ! r lL, j t r ( , j r i t t lL, isr t l r r j r j rLt

f r l . . ( \ lLr , . r l l , ,L l rL LL(f \ , , r l r . \ . r , ( \ t t , I I L . I . , I I I I 1 L L, I t \ i . . r , .\ t ,L l r . r r l r . r , i ( . r t , \ \ I | , I , r 1 i . I L I I I I I i I , j . lL\ . , , j I t \ r t j ( f r t l r l . r (lhr t . i lL rLir . l ( i l i . | r r , r l t l i , . ,L i | l r , r t . l . r ,1 !1.1 , r tL. ! r r l \ t . .1 lL l ) i . .

. . . .1] \ l t l L| \l )1, \ , , r1 r | rLr ' l i . I l l r ( . r r , , , | \ , r iL L L: t i t rL\ ] ,I '

: . ( \ ' . r . , , ( i , r l , lLr i r . ) ! ! ' : rL, |L(r ' t ) i l )) ( ,1, , r . . , L , r ( [ ,

j i l ,L '1, . 1, , \ ( ,Lr , l , r i , , , t : rL. t ,1, ,1\ i l i , t , r i . 1, ,\ \ t . I t .L, , IL1| , \ I . I I tL. ' \ , i , , l l I j j ILr l t . ! , . r i ,L,r l { . r t r l

L, j L) l rnrr j (LLi- , lL\ t LL, f ! ( \L l i r \L rL-.Lr l t . . r 1. . l r , r \ j , . , , r r . . . , r l l . t .

t l

l i l

: ) l 1l

| | i { l

l l i - l r )r i i l !

t3 i i3t3: i l133,1] , : ]

I

, l1 l

t i i t ,t . r . t '

.l1l

i l l t rt . i t5t . iut lt i i : ta

Sample Spol excharqe rnles

I

l

l i i3. lt . i l it i r : t lt i i i i /t i t . t l

l : :1.1l t3 '1l f l l l] l ] l t1t3! I

t i i : il l i i )|lit2t i i . t I] l t l

I ilii I I ii itllI i t , t i iu i

i t l t t i i i iI i i i rLr t i t . r i

I iiiI lu. lt i t i t l

|tit:-

XT I38 Stal s l ca Process Conlro

Sample Spol erchange rutes

1l12t3

l5

1T18t920

1341133113321334

1336133713411342

1334

r336r335r33513331334133813351339

1334

r336

r335r3331340r336r3391310

13361338r33l13321334

1338r33713381339

1334r339133413341342133713381339

I -s. lh. r l , r l , r l ( ' sc l up nr.nf nnLl r . r r rga.hnrts, in l ( , r l ) rot th. .h.r f rs i l rdJis(Lrs! th( u\c s 'h i ,h (o! ld L). In i (1. ,Jf r l r ts t ( ) r .nr of f l1,s.nr.r l i { ' r oft l ( Jr l r .lh. lo l l , t rv ing J i t , r t ! f11 ol , l I in, \ l wlrur nre.rsorcn(rr ts of thc z i r r.on(r f t r , rh(rr (m,,rs( | r1r l

. rs Prf . (nt . r j tc rJ l 1 in. sulph,rr( ,on s(r l iL r ls ' r lPh.r i ( , ) w.r l nr , rde in n ! is . , ,s( r . rvorr st jn L, , j ih thc nrr . r r r r r r lr inqr \ n lufs ot 20 s.rnrpk s ol s i^: . rR, gi ! , ,n rn lhe l . r t r t ( ,

Sample Zn conc.(%)

Ranget%l

Sample Zn concl%)

Range(%)

I23

5618I

10

697693702693694704703ta1701699

038020036031028020038025018429

t112t3

15

1Tl8

2A

705692700699708744697700T0l6.96

0230210280200.16o1l0250230 t9025

If thc (l.tt.r.rrc k)be r$e.l tonritlatemcan.nrd rnngechafrs forconholtnlgtlre pflr.css, d.'termhc ihc iction i.d wirnhg linrs for thc chirrs.l\hnt would \'our renctirD be to thc.lcvelopmcnt (h|'misr sctting.r rder.rnccof7.00 1 0.25 p.r c('nt on thc rinc conc.'ntrr hon in thespnr-baih?(Se also ( lhnpter l {) , Disc ssion qucst ior :1)

Process contro us nq var a0 es&

139 x

: . : )

'1r

Con\ cr l t ion. lcontrol . l r . r r ts nrc to bc usecl on. pr( \ .ss mJn t . rcturnrg sm.rLl componcnts

' \ ' i th n sPeci f ie. l l (ngth ( i f 60 * | 5 m. l ivo

iclcrlticnl nrni.hinc! irc h\lrlvcd in Dr.king ihc c{nnPonolt\ nrlrl Proccss.npnbi l i f i s tudl( s c.n l .d ( ,Ut on thenr fc! c i l th. io lk^\ n1S drt . r :S.r p lc s ize, , , 5

Sample numbef Machine I Machine l l

Mean Sange

Sange

r2!r23

: ' :

: L j lLrrg

ii|) 1059 9260 3/59 9l00 0l{i0 trl59 6t60 5t59 6859 5559 9ll6A 2260 5460 {i859 245U.1860 2(l6A 2159 5760 49

Mean

60 {1659 t0ti0 3260 0558 9559 t258 8059 ti860 l460 1t66t 05rio 8.16t 0l60 82

511 015{r 0859 256t 506t 42

Ranqe

0,10l it l

0 l05

ULJ0302a2

0l;05tJ la2

:;

l23

5lllI

IUt l12

l , l

1/

2A

25

30

?4?T1i34l / -t5?3

3336031,1

t532

l r l

( r l .u lnt f ihe ((nrt f (n l i r i i ts h i I ) r uscd ( t r i nrhrr . r r l f rnge ( lLrr t t ( ) l( ! r .h In. .h nc ind gi ! . t l r ' r l rs(n\ l { ) f rn\ (1 i l l .nr11s l r .h\eer ltherr i Cotrr | . r f , , lh. rcsLr l ts f r )dr ( i .h nr i .h inf ! \ ' i th t l l ' rPf114,f ]n l |.of l ro l .h. f i l inr i ts. l l rd thf spfc i t i ( i t i { ,n n) le n.ot .(So| nlso ( hrpn'r l (1, l l is .usslon qrt st i ( r r 5 l' l he [o l lor ! inS t . ]bk gives the n\ ( r rg. \ \ ' i r l ih i r r mi l l i r r r f t tes for r . rchof 2t l s.nrt l ( ! of i i \ e plnels 1|sed in th. nrnr lLr i . rchrfr ' ! r f . r donrcst i .. f f . , r . ' l l r r , t i ' r ' . ' l . . '1,- | l , .

'1. ^ i ' . r

asn i 40 Sldl r l ca Pr0(. 's5 C0nl o

Samplenumber

Samplenumber

Mean Ranqe lllean nange

l23l56/89

IJ

42426l

32580a59g5

t l12t3

t5t617

1920

3.83l35315.81.62l511l67

550.8552.7553 8555 8553 8547 5550 9552 0553155/ 3

551.7561 2554 2552 3552 I562 I559 4555 851i 6

( r l .L, lnt( , th ( ( ' r l ro l .hr , i l i rn i is t ( , r i t r ( ,Shc{ l r . r f t .h. rs.rrr( t I t ( ) t lh,v,r l r ( \ ( r r l l r ( .1r , [1s l f l . r f r . t ih. R.rLr i ts ( ; i ! . ] r n \ ] ! \ . t f , r r i ( jn ( ,1' ,10

- | i r r , f l , I i Iur t { i r r rh, . . r | . r l r i t i t \ , , t l l i ( . t , , , , r ( . \s

(Scc r l i ) ( hnpl( ! , ) , l ) i { ussl t r r ( t rk,s l i tn 1, . I r ( l ( hJf i , , r t0. t ) is(Lrrs i ( j .

Worked examplesILathe operal iot l

r \ f ( inrp(!rr ' l Lrn\ l . rs , ' l ) .1I o l , r l ) ( rs. f r Insnr issi( jn L r i r is nr . r r r rLt . r (t rLr ! l r \ ing, i l . r lh( l i ! .nt ! s. l I f l ( . \ . f . r . t r ( i r 1, \ . .onr l { , ,urrs, , l ( . l r t , r rr i h.r l i h()ur l \ in l , .^ . r ls . l i , r t l r , t r r t )sr . r i ln. , r l !1 nrf .s i ,nr . l t r { ,Plr \ fsr, re.rrr l l ) 5 iorLnr l lo t r ( . la l ) { )0Lrf , wr l l r r n{) |1 j r . r l ( l is t r i l )ut i (nr ( j l r l r, fsul ls rb(, ! t l | l nrr . I r , r r r ( | n r i r , . l r snnrpl( , r , rngf i ) t r l l ) 00t)7.D(r) L sr t l r is in lofnr.r t i (nr to st l uf s( | i l r t r l { , ront() l I h.rr ls.(b) l l lhc r l \ \ i l r ( l h i l . r in.e is . l 1t)r j .502fnr, $ t l Ls \ our r1, . r . l i { , r?

l \oUld r{)Lr . , )nsid. f . rnI r ( t i t ' r fe( .ss,r f \ l(s.(

. lso( h.r f t r ' r l (1, Norked cx, l lpte l )( . ) lh( lo l l (^ i i11g t . r t r l ( ,sh()r 's thc op.f . r i , ) r ,s resut l \ o\ef rhc dr\ .

l hr f re.rsun,nr( 'nts t r . r ! t . rkcrr Is ing.r conrp.r f jhn. ! ( , t t l , 3. i ( )0.r j rrn, l . r ro r l l ( \ \ 'n in urr i rs oi0.00tcnr r f nrr , . rns,r fd r lngcs h,r \ .bLen artr let l to the rcsul ts l \h. t is yoUr intrr f r fhr t i . t r r of th. ,s{ ,fesLr l ts? Do \ ,oLr hdvr nnv ( .onnrrnrs ol l the f roce!,s rnd/or th( .

, r t I r ,Lr I l l l v

f l ranrd r l rL ' ! r l : i f raor( i f ( l l r r t i r

Time123

/11,r . / r r ' r i / r l l r r / l r ) r , i , . ixr t , r f r , / i [ i / ' r l

, l to

r i l l l

1l l

l l l : r1 l l l2I llll 1r 1l

l f l 1) l

| , I r

r r : l ) 1 l1,i l l ) l ) I

2r l l l r l

l r l

t .1I lt ) !

ll

t ,L) lr t l|2

6

lt l '1 l l

1r l l

l l l | l

I t l

11,

Range

t , , '

1l il i ,

1r i t

' ] ,

L) l

L)

I l

l L l i / j r . , / r l r l , : / r r1 l r r r l r r r r , r r r i It , t r rl l

r l 0t\ , i , . L l i , l . i r l ) ( Lr i f , , ' I i , , r I . r ! l 11, , t ' , , \ i . . : i r rL. , l .L t , , l

\ l ( , . rbr i i r f l ( r f l tL

l , , , , i r \ t , f ( rL l i \ l i l r '1 r . \ r ;s. ,L l l r - \ .

\ I L r i I i ( ( ) r r I | , i t i . fL . r {LLr l ,sr l r

l , ln r , rL Li , n, l . \

f fL r \ , ! , r i , i r f ' r l . \r l \ / i l .1r t j ' : r j i r

'lrl& t . tz Star st , ' r p of tss con1r l )

l . ' t r ! ( . f \ \ r f r i rg l inr i rI t \ ! ( . r n, l ; ( i f inr i t

2,/ l , \ , i i l . {ee7l.rrr,^ , l i I l r )1)a9.nr

\

-

I r i , j r ' \ l , f , .n( l i \ ( t ) , , l ) r , t ) , t r t lt ) , . I st t )1, t . .11

l i , | '1t . i , ) | l r ( ) l ( .h,rL ss, . l Ut , r i l jL l , l r , r , ' . t i r i r i i t t ) i , / i r ) 1|) l ( r ( | jI t l l t r r , ' , , i i | i t l i i i r l ) l . / i l ) t ) i ) l t , . r ) rl , j$L r $,r , j j i t l j j j r r t ) / i l r .1)1l l ) i ( r ,I ( )s1 . r ( l j i f r l | | I t ) l . / i 1) l ) | t r t ( , j l

( l , l l l i t i , i \ ( \ ! i \ , , ) ( . t l \ ( . r r l , ( ! l i t 'l i " r ' , \ f l ! , r r l i \ l l / I r l r ,

' i i / { l l l l ) l ) : / I l l r , t t r ) l } l r l ( r

i:il;lili0 002

n ou, I

i ,rE

LAL

99^:9s99.ooo---" j___. j

d

r4 i r rLrr r r in i tL i I | .o.nLr l

Prrr . r . r r , . r l ,0 L.r fq , r i r ih .s l l3

l lk t ro( (* ' is n r l , r l is t l . , r l ( tnr l o l , f rL i r rpr t . i r , l r r r f r f rn, l r r r : t ,.hJrtr , r . !sf{ l l ( ! l \ r ( i f l r ( ,1, \ ! r i r l iJ f l , l r rnsf : .hoLrLl l \ ', l . l f ( t r \1 l .v 1l l , r ] r \ t \ rnr f . l , , l . r r , i l lL.r l l , ( , , l r . r rs. . \o lLILh( '! f r j i . , l r . r l ( , , i ( l i t f r i . ( { r !g.r l f r l

1, I I l r ' nr f . r i r \ . r r r l rJrrgf : ,Jr Lh r . :u l r , r ( .gr \ f f n l ln,Lr l , r ' r l !^r ', i f ( l , I . l , l t ,L1(t l ( ! r ( t ! r l i rJ ( l r , r l r i r I : i t rLr . r , L I

l l lJservi l t ofs 0n t lre c0ftr0l clrarlslh( l r l l ' . , , , , t 'L( , . r lL, r L! l , i , . l r ' , i t i i , , , l , l ( lL, l t l ,k , r , lLr r ! \11! , j i , , i ll l r ' , , l r ' , i l ' . , r ,1,1( , r1 7 r i . . l r t r \ . ,1 l lLr l | | i , r ( I I r r . I I i i , r I I \ \ , i \ , ! ! . \ : , i r \I l l i , . ( r l ) l r i . r I r t , . i r ( r i , , $.r ' \ \ i l l i i , , l l i r ' \ \J i i , i { | , i1. . l1r t $, i . . l rLrr l l l r , . r r l l I r , r r l ( isrs,rr l L( , f ,1 l l { t ' t ! r r l , ) r L( i r t \L\ L l t ! L l ( t l t ,l , r { , , i r ( l ! fL : , f r t , f Tl , ( , l r r ) : r i i { . , r r r , . r l l L l i f . l l r l (11 , r L l i ,Lr l i lL\ , r f r i r . r rL ( , i l ( , r i i , r r i ( t l r L l r r , ( l ( , t r rn.r ( l I f rLI , i fL l , i ln ' t . l l i r I rL\ , r f r i t l ( i r f \ , I I r r . I I r i | | rLI I I rL.r i . , r )$.r ! I i ( , rL lL i rL, r rL tLl l i , r ( , , r r ( ,1 Ll ! l l 5: , r f r f ' ( s,r ' l jL l r i l i n,r .Lr ," , , r1r , \ , ,Lrn. I j ( , , r r, , , ,1 . r ( , r l ( l l i . r \ f i t r r r \ l I rL f , l t l l , ' , r , , t ! , rL \ j r j r | l ( . r r ( l , r ,Lr , rL l tLr ' l r r ' r l l l r ( , , r ( l iLr . lnr( , f1. l r ( i$t , \ ( , r r l i ( l r ! ,1 , rL l \ ( r \ ' l \ . r l , \ l

l l r , , i l r , , l , r ' l l rL h.r l , l i L( , i r l , (1, ! , r l l l ' r i \$ Llr i . t r \ i l i , , t , ir i ( l ,Lr r , r l ) l ( . ( ) , ( , . .1, , r1( l r\L l r , | , lh. i r , ! i i r i ( . \ ' \ i f ( r , rn\ i l \ r in

- tet i l a0l tct ! ts 0ns(1 LI rL( i l ln l ' rLtr(* ' r j rLr j f ( lLrrrr i rL l ! r j j , r j , , r ,

( j i l r is l , , r l ( i l r ( (1f l11(,r : l r r L iL l l , i l r ( . ( r i \ l \ ' r ( \ l . r rL l , r l ' l r . i f ., r \ . !Lt , l . l \ \ l l ( i l l t \ \ i f i t l r ( . , rL l rLr 'L r ! r l . rL ' , ( ) i l l r t , l \ \ , r l , , rL ' .L ( l l ! , r \ ( , : l i ! . r lL\1.

' r r l r 'nrr , rL r , \ l in ( t r rLr) l L l r r , r i t l ! 'L Ll ln t r r ) l ( . l \ . r ( r l \ l ! r r rr i l t rL l lL l l l i ) / ( . r . , r \ i . lh( . i ) r i r tLr . i f r \ ( \ : ( , '1. ' l . r L\ \ lLr tL\

, , t ! r . r1( ' r : . rLt( , is$(, . (L, , i r \ l , r , , , l l )L, l ( f , rL\( , , : , , i , r (L l ! , . : ( , { , rLi : , g( ! ! l , i t r ' , fLt , , n l , ( ) , , , . , \ , , r r r I l i l l , , , , ( i ( 1, . r r i ! . , r i , , ,1. , , , , .

00ntfo 0f d sso ved for in a dyestu[ f. , , i ( I r . i , r l l ( | r r ls in, l t , l \ ' r \ \ l lL,D,r i f l . r i r , ( r r ln ' l ( r r ( l is . .L, l \L\1

. , iLL(.n1(Jl i ( l \ . \1| l r i ) rnrLr l . r l i (u i . p,r i1s l I r r r l lLLi f l f fnr) \ r1( . f

. , t rLtrLps ( i l r i r iNr ' r rn r i r ! r l : hr \ L l , . .n () l .h i r ( !1.

&a

lrrt) r.Ll I R. 8,1

nrfnn ot / th srb|] l r [ rprnfgc of l lh sUbgrou])

( . r ) I l .s ign thc .pfr) f ' r ' jntc . (nr lnr l chnrrs.( l ' ) Ih. spcci f i f . r t l ( l r (nr thc proi-15., . , , . ,u; ." ' ,n.r t no nroro thnn lspt)m

rl issol ! r ( l i r ( ! r bc I l s . | t i r1 lh, , i r | ru l . r r i ( ! r Assuntng,r r ronrI l r t shlbLr l on nn( l th i l lhc p({ .ss cor i t in lk,s l , ) b( in s l i r is t i f . r l .onin, lt r ' r th rr) .hnni+ i ' r . r ! . f . r {c 1)r d ispf fs i (nr , i ! h,r t pR,P( j f t i { ) . of th, in( t l\ r r lLr , r l nx ' , rs!r .nr , f rs | r r \ , l ) ( ( ' \pc.h\ l I j e\ .NLl lh is spc. i f t . i lnDl( !d i l \ ( ) ( l r f f l . r r r , l ) rs.ussi , ! rqurst i { )n5.rrd(h.r t t r , r 10, \ ! { ) fk( ,1

Sol!t ion

I44 Stal s1 ca Process Contro

\ ,R

).r' ,!lll5

( , / , l r { ,nr At) | r , i r l i \ l l

ll , , ,,,'''',,j.X" | ++5 rfnr

) .326,, t

I l l55l , , l l 61(r L)rrnlv,, J5

UPfcr A.t i0n Lin(Lflnr ['.rmnrg LDre

X 1( l ) .Sf l15 (; (3 )< 0 6.16)l i .7 in( l l7 5 ptnrl5.rr : (2 ). (l ar-1at

= l .1.3.rnd 16.9Pprn.

DiLr LR -

23.1 ;336=79ppn1DL,, ' i R l . l l l ) (336=6. lpp

. iSrL

| , ! r\ l , . r r r . r l \ . L, i l . Lr l , r r rL i r i . . , , \ t ( . ,1r i ( t i . i ( . , , r rL i l I I iL. .

\ . r i , I l \ , , i i

Lr I l \ . , j r I

I r , 11r . i l r .

r r , 1 l i iLr l t i l

\ l , t ,L i , l \ l r

1 \ l ' t ' , i , \

l ' l r l r rnul lo l to

r i ( . . r1.1! | r tLr l \ i . r i r | tL j . : l r , . . t r , . j \ t . ,rLr iL . l i r ' . r r lLr l i r i r r r r ' r . l , r lL l i l i ! r r i r I r r l L r . \ r i . r1 , r ,

\ r i r ( r r ! l i , j lL, r1r j r , l ls Lrrr j r \ rL! . . . r j r ( r I j r l, ,1r i , t i lL, I r1r , , r r l I

'

) t

' ' r r i r , i l r ' . r

r l ,L r j t |1.

.L r , r Lrr . ! . | r r t i ( j | ! .

( \ i r { l l . r ( l ( l , . , r i r i r ( r .L i , -L, j t l r , . r l i . . r | ' iL. , . l r r I \ i \

' .1 Ll , r i r . r r . r rL l r ,L i r t , L r . l l l , iL1 r , , 1r , . t r , l r , , r I j . l rL,, lLr , ( t I l ! lLr iL (( r r l l r ( . r . lL j r j j l , l , j r r l r rL L I l ) rL LL,]r t r . L. r , , I I I ! . l jLr l , r l' I i , r l l ! , ! i r . r r L, l l l rL. l , j . . r \ , , L, l r , , r ! t | | . r rL. tL r . r r t tL. | r tL l l, I I : \ I I . 1 I r L . ! I I I \ r lL, i r r l i r L: \ \ l ( r l i , . l . : , \ i . . . i , l , r , , , r r i , , l

' r , 1, \ , .1. . i , , ,11(.rLt r l lJ \ l ( , i , r l r r : , \ L. j ,r \ l ) r1 , r1, , L l l , i t , r . , r t , l rL t ! , ( ( l . , . r , [ ] ( , t r lL. l , , . I i ,1.1, , , \ . . .

\ t r . r r I , : I r , , L | | ( L l , r r l l 1, , L l : I \ r 'r \ l i , r l , . l i ( . t . r t , i . . , | , L\ t r . r \ r ,L,r , i ( 1. , , t , . r , r .1t , , \ i , , , ! . , , iL r , ,l i , , \ t , i l , , j l \ lL i r t ( , , t iL. i l . t r i 1, , , ,1, , \ , ,1 1, i , r . , , ! .' .11 , \ , , ( i , r l l , t ) 1\ i , [ , \ { \ . rL i . ( ] l

&I 14 Slat ist iDal Process Contro

So ut of

( . t f x, = l6.E8cm.t=No.of \nmples 20

: x,lr !!ll! = 0.811cn.,

; n,7* = '1,11 o.ooz.-.

A.t ion Lines.r t

-

A.R 0.831 : : () 5.r1 ) i 0 007)Ll t)pcf r \c i ion l . i r r f 0.83i1.nll . (Ncr A. l(n l - i c 0.130.nr.

lviDi|g l-incs rr , , 2/t Arn 0 li:t.l () J77 ! 0 007)Ufprf i \ / . r rn ing I infl . ( ) ! ! . r \ 'V.r fn ing I i r r .

I hc Ar i r r l 2/ l c()nsh r is . r | . ( ' obrr i r r \ l t f , !n A| | \ rk l ix IJ

Llpp(fA.t i (nr l . in( . r t t )00i l i 2t . I i0.007 00t6t .nrLl t )p(r l \ ' . r n ing I i f ( n i l )1, , , i / i l f t l )

tx147 xProcess contro us n0 varrables

. 0 81 0.837l . \ ZLL. - 0 003

lhcf . f ( ) rc ' pertntngc ol l ts i l l r Lr f l l 'e f t ( tfan" \ \ ' i lL i l rcre 'sc n) 15 87pef.cnt ( f r ( rn APPcndix A)

_ n l l01lr l ) st

-

r / \ i [ = =_ 1] . ( r r r l lisUpt.r Wrrnr lrE Ll ,1c (UW L)As / , UWl, lhc Probnbi l ih oi s.rnrPlc Polnt l ' ( i .g otr is ldrU!! l ( l 5 (50 fr f . fnt)l lnpcr Acl ion Lirr( ( l lAl l

0.s18 0 l . l l70.t t ta

' lh , r . l ( r ' i l forJr h l ) l (s, f fo l rn l ' i l i t \t ; , \ t . 0 2206Ihrs, t l l t IRnarL, i l i t r ( ,1 ()hsc, \ ' l i r l lth, t iF i snnrpl( n ih ' f th i .hfr t i t t is :

0 5( l ( \ i ls i (1. $ntrr int : l i r r ' (511l l . l20(, , { r ts i ( l , f r t r , . l i r r ' (12

f . r . . r i or I in l )i f I5)

4 Bale werght( r ) L ls i Igt lx Lr,r l , ! re ig l r l ( l i i rbelos, . r l (Lr l r t ( 1h. . { )ntRr l l inr i ls l { ) l

m ,rn . r r rd f . rn l I ' ( | . r f ts i ( ) l r . ustr j \ j lh t l i r :c ( i i1, ' .( l ' ) t .srng t l ( 5c ( onir() l l inr i ls , lL1, l lh, nr . i r i r r r l i 'n l - . \ r r r t \ t ' r l ( )

( . ) ( ( ! rnrrnl (D t ln ru\r i l is { )L, lJ ln.Ll

Bale weioht data tecord (kql

l l r

Sample Timenumbet

4 Mean X Ranqe W

10 18 34 0710 03 33.98r0 06 34l910 0s 33 79r012 33.92

33 99 33 9934.08 34.1034 21 34 0034 0t 33 7733.98 33.70

310,1 0 1334 04 0.123415 02133 85 42433 81 0.28

(co t nled)

311233 9334 0033 8233 74

&I 148 Slal st ca Process Control

Sample Timenum0et

lvlean .Y Ranqe |/y

6T8I

10

12131415t61T

t920

0.220.500180.260.640180.130.210304200.1s0184320.05016

10 15 34.0110.18 34.0710.21 33 871A 24 34.A210.27 33.6710.30 34 09l0 33 34 3110.36 34.0110 39 33 7610 42 33 9110 45 33.8510.48 33 94l0 51 33 6910 54 34.0710.57 34 14

33 98 34 2034.30 33 8033 96 34 0433 92 34 0533.96 34.0433 96 33 9334 23 34 1834.09 33 9l33.98 34 0633 90 34 r034.00 33 9033./6 33 8234 01 33 7l3411 34 0634.15 33 99

L:

;

Ih

(b) rh((c) corTh(

34 1334 t034 0534.1834.3134 1134 21341233 8934 0333 8533 8/33 8434 0834 07

34 0834.0733.9834 0434 0034 0234 2334 0333 9233.9933 9033.8533 8l34 0834 09

I0rAL 680.00 4 66

Solution

. . , i ( i rnn( l ( l ' f t )cfss) M. i f 1ot.r l of thul l l . r ' rs (X)Nunrtr( f 1, f s impl( .s

660.0r)20

r l l ) l r lg.

= r.14Il\!rss1R )Nu'nb'cr of s.rmpl i ,s

,r l

R M('.rn ltrnge

tLrf sJ'nple sjzo ,r 1, Ll,t 2.A59d 0.233/2.{159 = 0.t l3Stand. rd Erf tr = o,/ \ , t 0.113,, \ ,T- 0.057.

Aciion Lincs: t a 3ol'\,t3.1.0013).0.057

= 34.00 -

0.17

!*Pr0cess c0r l ro usrns i .ar iables 149 X

34.2534 2034 l5

34.0534 0o33 9533.9C33 853380

'lit 11213 14 15 16 17 18 19 20Fiqurb6.15 8 1L i l i lLL f fef , \ ! l i ( r r l . i r r ' l . l LTlgl .ow.f A( i i ( r r I i r , : l i . r l Lr

l \nr . inLl ines \ l . \ , rI ' l r ) r ) , 2 .0r)57r.t r)r) , 0 |

t lPfr fW.rrnjng l in( i l l lhgI r )wff I \ , r f l rLng Line 3.1 IJ9ls

I h. Incrn () i th. ( hrr t is s. l Lr \ , th. spc. i tk l t i (nr { r ' t . r rc( 1 nr( \ rn

\ ' l imi .g Linc

The d. t , r nre plot ted in Figurr 6.15.Conlments on thc inenn.rn( l rangc chnftsThe tablc bclo1{'sho$,s tho nctionr ihnt ()u].1 h.rrc bcen t.1ken hadLhe rhnrLs been . \ . i lnble dur ing Lhc t fo( lLrr t ion fcr io( j .

2.57 ii == lg lR

2.17 )i () l:ll -

0.59t) k8-.

I e3 ) :0.211 = (1.1i( lkg

aI 150 Stat ist ical Process Contro

Samplenum0er

Cfta 0bserualion ldleryrelali0n

fuleaf

lllean

[,lean

Range

Fanqe

Ban0e

uppe. warn ng

Lowerwarnrng

Acceptable on ils ovrn resamplerequ red.Two warn ngs must be in the samewatnlno zone Io De af acnonresamp ng requ red. Nole Rangechart has nol picked up any problemAfi0N

- ncrease lve ght sett ng onpress by approximale y 015kq

Acceplab e on ls own. resamp erequlredNo action requlred samp e 7 was astalrst ca evenl.Poss ble aclions could involveoblain n0 add I onal nlormation butsome poss ble act ions c0uld be(a) check cnrmb sie and I ow rale(b) clean bah prcss(c) clean iabrc balc c canerNole Mean chal1 ind cales noproblem the mean value lilrlletmean (Th s emphasites lhe eed toplot and check both charls )Decrease we qhl selt nq on press byapproxnrarely0.23k0Acceptable on rls o\!n a possib edorlnward trend s appear nq

ACr 0Jir ncrease r1/e gfl seit n0 0rlpress by 0 17 kg

l0

Second lowerwarn ngoul of control

No warnrnq or

12

17

[i]eirn

[4ean

Lower!r'arn nq

Second ov/erwaln nq/aci0n

18

II

xI re,l

IT

Sta! sr ca Process Conlro

understandablc, simple compLrters/cnlculaiors have made thc usc ofstan.lard dc!intion charis morc acccssiblc. Aho! e snmple sizes of 12,ihe rangc ceascs to be a gooct measurc of sp(.ad .n.:t si.rndard dcvi,attuns must bc usccl.Standnrd dc!iation charts may be dcrivc.t from bothestimated st.rnd,ard dcvjatiors for snmples and sample ranges. Stanclarcl dc!iniionchafis and range charts, \^'h.'n c(,npafed, shorv littlc diffcrcfcc h co'lt rol l inE vari .bi l i t \ , rTcchnqL,cs dcscribed in Dona kl lvhecl(,r's hook are a\?ihblc f(rr sho.ipllrdllctn runs. Tlese inclLrdc diffcf|n(e ch.rts, which arc b.rsrd ontliffcrences fron t.rrgct or nominnl values, .nd \'.rrious f(,rms of Zchrrts, based on clifforemc('s .rn.l produci stind.fd d.\'iatn)ns.Whcn consrdcr ing thc nran! di f fe.cni typcs of conirol charis andp()ccssrs, ch.rrts shoukl bc sck cted ti)f thi.ir casr ofdcte.ting chnngc,c,rsc of Lr l ldrrstrnding nnd abi l i tv k) impfo! f pr ' (Jccssc\. With ni tufnihgrolrpecl or pnsl di t . ] cor l !cnt ionnl nredn nnd r.rngr ch.r f ts shoulLl brus(d. t roronclr t-d l im. ' ( l . r t i r , indi i idur l ()r rUn) chir ts, nn^ ing mfJn/nroving f ing{r fh,rr ls nr( l l i \ !MA chir is nr.rv bo nrorc npt)r( 'Pr i , rh .

Beferences and furthel readingl l . rn l l ,N. . rndl i , fA, l l l l { le{)+) 'A(L)n,p.r f is(Dtn\4, , , , , , , , r1t innge(h.r{swtr t i

l le ( { r r1 i )L l ln! inA l ' . r . tn, , l r , l t . i \ r . . r ( r Sh( l \ , , t t (n l r t r1rnr ' , Qrd/rr lr r t t Rt lmlt i l i t t t l ) t t1 i11)nt ! l i t t I t futL\ td! , Ur l l l r . No.6, Nr^1.n, l r ( r / l r r \ . r ,Lr f f ,

l lhol( , K I t . (Lt)91) (()r lF ln i l l r )25) L{, / , / ( ra j Orrr , / r / l /5rr ! r ) , \ i ! , 1 ' /t \ ldtrr . r t \ tn l \1ukt t t l l t \ \ \ t t , An!r ' i .nn \ lnnJtrmrrt Ass(\rr t ion, Ne[

r lunt(r , J 5 1 l ! f i6) ' J h. l i \p( in.nt , . , lh wi i8hleLl r" l , ) \ l i6 / \ \ e, . r8r ' , / , r , , / i , /Qrtr / i l r / iJnt , \ , \ l ) l 18, |p.2() l 210.

wh.f h! , l ) .J. ( r . r . r r ) Jr la r lLI 51,r . st , ( t t f s5, Krxj \ ! i ] | ( , r \ , us^WhocleL, l).j. (2llll.l) ,,1,fud,, f,1 /irl(

' ,r

-!/,C, SfC fn'ss, K,r)\! ill., I N, l-S,\

Ir Discussion quesl ionsI Co'nmcnt on the st.ricmcnt, 'd moving mean chart arrrl a ronv0n

tiolral mean ch.rrt $,oul.l bc uscd with different typcs of proccsscs'.2 Thc data in the tabte oppositu sho$,s the lcvels of contaminant in .

chemical prodL,ctl(a) Plot a hisbgram.(t)) l'lot.rn individuuls or run chart.(c) lllot noving mc.n and moving rante charts f(tr iiouped samplInierpret ihe results of thcsc plots.

*IOther lypes oi conlro char ls ior var ab e9 185

Lvels 0f contaminat on n a chemlcal product

Sample Result (ppm) sample Resull (ppm)

123

56I

I

t112l314

1Tt8t9202122?3

?5?6212829303l32333,135363T383940

404.9402.3402 3103 2406 2406.2402 240r 5401 8402.6102 6

416 5418 5,122 7422 i404I1A12,104 I412 04120405I404 /103 3400 3400 3400 5400 5400 51A2 3404 1404 l403 4.103 4402 3.101 1401 1406 0106 0406 0

,1142.13

11484!505l52535455565/585960

62b36.1ri5

6l6869t'a11t273

7576T7T81980

.109 6409 6409 7409I409I410 8410I40ii l401 3401 3404 5404 5'104 9405 3405 34r5 0415 0107 3399 5399 54051105 43S/ I390 4390.1395 53S5 5395 5398 5400 0100 2401 5401.5401 3401 2401.3401.9401 I404 4405 7

&t 186 Slat lst cal Process Contfo

I h . bai.h minuf.chrrhg proccss the viscosity of rhc (ompotlndnrcrc.scs dLrring the reactnn cv.l( .f 11 cletefnines thc md-p{)intol iherelc )n. Samples of thr. cofirp(Nfd ;rre likcn thrcughour ihc $holepfrn)Ll of thc re,lction nncl sc t n) thc l,rbor

,i0lher l t " 'pes 0l r0r t ro rrar is for !ar ib es rS7 X

Is lh.rc,r s ign fLc. f t corr f l . r t ror) b| t \ f f r r thc 'sc t t r ( i nr , , . rsurcJ f . r r . r f rc l (Tc) l th.s l \ ' ! i f i f . r i rof ior \ i \ .osi l \ is+5l l0 torr l l01),rrr l ( l th, nr . r (uf . t ) Ic l l f i r f f rn!orhe rsfd nrrr i l f . t l \ r .of tn i l , ) t t l r ( p( \e ' .1l h i . i ln lvsl r (Jr i i l r i ( l b.( l f l n. l , , r \ tn. t i f f ( l ! f \ i r i r r . 1, , , t , h. ' . | r ( lLrr .don(, , r1 , r l i . r r ' ( i lhoLrrhlor( l r r r l ( l f , rh\Jn, tL,r . r r ) ( l l l l ) isLrs( ' t l, 'sn. . r ln l \ i r I r r . . r r rnfs() \enl | \ r i r is l lx rnr f r l ,1rr i , r i i ( ! r (s lNl j ' )sr( . t .lh( l i r l I r l t , . .L,rs,r rs l , . r I i l , rn! l r i r l , , r l r ( t , ) r ( \ i ' l l l ! ,s(J l l ( l 'L l iL, ls{rptnir l I l s() l i ( l ( i r r l \ \ r i \ l l i . r r r r \ l I r ' ( r l i r l l r . rcJLr( l i . | ( l i l l ) )s l ( f r \ i r r t , r l , rNrrrrLrf , r [ \ l ' l ln. l l l l ] ( . \ , .1 , ' . , r i , , , t \ ) , l . I rL I r { r*ql . f inr t l , . f , r r ( l i \ In( . , r { r f t \ l ( lL i rnr l l r ( . s l \ l l ' , r r ( l l i l l ) \ lng.sl l r { 1( , l ( t r \ r f i tLI , r l , r $( , , . ( i l l , \ ' l , r l , r r l r r I l r ( \ t )n, , l r teLl , l r r r r r i r r r l ,Lj r r l r l r l r r r , ,1 , r n, \ \ . r l , r l \ \ l r . r i r \ I r ' \ . ( l . r t . , , r ( uJ. l l r ' l l l l i ( , \ .( r je.r l . l j l , . r l | l r . r l thrs l \ l l ' \ l . t1.r , r ( ] 11j , . l l l l lL\( , lL) | l lL j r r , r l r ( \ lLr(( \ l

l j t q l \ r r l r . r l i ( i fs , rn: i / ! i l : l| i \ tNl t , L.() t l| i t i t t ) th e,

Balch

llll

2 l1)

l i2

t i ) i l

t,li1

tidi

3693i0

t l : '

t,l .l

r3 8t3 9

THF FED

111

1t 5

Balch

:tN l

iiti)

ul l ,

39rl39!10u

THF SIIMP

tJ 5

THF NtO

t1

t i ;] l ]

x! tae Stat sr ca process control

C.ru1.ou1.,n onn1u"'" of this d.ta for rhe IHF le\cls ai the SI\ Ipstcpr lJ | ,J t .n. , l Rl f . , ' ' .1 ' * ' . n! Lr . ) r | | , - . t . , r . , h-r , . r . . . i . .c l , r . -\ . t , , , inJr,1l . r , I t l \ . r . rLts . r t . I F. $. . . , r . r . . l . . e. i .

Assu'ne th.r t .endlngs fronr frc ln)us srmit i r c.rnpaigns hrd gl \ . fthr fdlor,|ig d.rt.r:

] 'HI,SIMI 'Tf I I j l t l r t )

l l U(, .0.1(r50.0 30.

5 Ihr wofkly dfnr.r fd of . r p|1)ctu. i ( in nnrnes) is gir ,on t rctor, . Us..ppropnnh t ! .hnrq'rcs k, in.r l \ ,s. rho drLr, issrnr ing th. t infornr ii r ( )n js pr ' l , \ id i 'd nl the (rr( l o i e.r . t r s, . ,cf . .

l l

t\

I2

56

9l0l l

l3l4l5

17t8t92021222321

Week

?526

t829303l32lt3343536

383!l

1243

,15464148

Demand (Tn)

85I

8B5

r05

l lt5

6565t i5

65II8756576

Demand (Tn)

8i5

65r05r58

l0

45t0 585

t5t05l0t5

t l5595595T

\ lJJ,r i r , - \ \ , t r r ( . .n r , r , \ , r - .1, .^.- , . t r iu. . r t t r . , r . . r . . . r . . .Jtr . . . , t -nrcnt rvorks, into thc Ri \er Nl i . : ld U.ch da),n sanrptc of c l js( . l r . rg. , ist.rkfn .u.l an.lysed to dd.rnrine thc.m ()nia conk,nt. ttesulrs fronr

r 89 I0ther types of conlrol charts 1or !ar ab es

thc dai lv snmplcs, ovcr . 10 dav period, are given belorrAmTnon a content

Day Ammonia (ppm) Temperalure ("C) 0perutor

I23

56T8

101112

l5

IT18l9202122232425262/2829303l323334353637383940

24126020926.225.3249235212238215230272225244275t9l2t4269?882SS2T l)26./25129628226.729.0221233202?3.518 621223.4

21518.624118.2245

t0l61113l71212

t6t3l01ft0I

1l1081

lr ll l

1I

10121512

lt111l121913t113l6l l12

Use suitablc icchnic:tues to.lctect an(t clemonstrate chrnges in anlmo-

(S( 'e . lso Chipter 9, Discussion quest ion 7)

xI 190 Slat is l ical Process Conlrol

7 Thc Natjonal Ri|ers Authority (NRA) also monitor the discharge ofcfflucnt into the liiver Midd. Th NRA can proscute the Water com-prny if'the ammonia content exceds 30ppm formorethnn 5 per cent

Thc c rrcnt policv of Middshire Water Company is to achie|e a meana m mon ia con tcnt of 25 ppm. Ihcy bclicvc that this target is .1 reasonabl .ompromisc bc'trvccn risk of prosc.uiion and excessiv use ofelectrjcity h) n.hicvc an unneccssnry kr\{ levcl.(a) Co mc'r1i on thc suitability of 25ppm as a tar8et mean, in the

light of thc dav io day variations in th data in qLrestion 6.(b) What lvould bc a sui tnbl . 'hrg.t mcan i f Mi(tdshire Water

Compin), cou ki bc confidcnt of gctthg ihe proccss in control b,vel iminat ing thc kind ofclrnngcs. icmonsirnted Ll t thr ctr t . t?

(c) Describe the typcs of.ontrol chnrt thni .oul . l be uscd n) monik)rthe.mmonia .ontent of thc cf f lucnt i rnd .(nnnient br icf ly on thcirrelat iv( mcri ts

8 ( .r) I l isfuss thc usc,) f .ontfol .h.r f ts f(n f tngc'and srnrdnrd d( ' \ , ii i ion, cxplni f int thoir di f fcrcn.r 's . rrrc l mc'r i ts.

(h) Using p(xtss .r p.rbi l i ty stuLl i (s, pro.csscs m.r)r bc cl . rssi f iod .rsb( inB in shrt ist i . . r l . (nl t rol und . .rp.rbk. l i rpl . r in thc b.rsis nndnr( 'nnin8 ol this.Lrssi f i .n in)n. Sug8esi .ondit ions ur\der whi.hcontr) l .hi s Innv bc uscd, rnd how thev n v t 'c. t .hl . tc. l tonr ikr us( of drt . r $ hi .h nre nvr i lnt ' le,nr ly infralucnt ly.

II Worked examoleUv.n .nd f lunrbl( m.n1ufr.hr( shrnprD whith sel ls.rs.rn own'Lrtelbr.nd in thc Ask&ry ch.r in oi supermafkcts. 1h. sh.rmpoo is Inrcle intwo st.riaes:r trnt.h nlixirlg pro.css is f(nl('sed b! J bottling pro.ess. lnchb.trh ofsh.rmpoo mi\ lrLrs a valLro of 110,000, onlv on.'b.rtch is mixcd perdnv and ihis is slrfii.ir11t to fill50,000 bottl.'s.

Askway spc.ify thdt thc ncii!c ingrc.licni content shoulcl lie betweenI 2 per cenl nnd 1..1 tc. cent. Aftcr nlirnrg, a samplc is t.rken fron ihebitch and .n.lyscd for activc ingrcdirnt cr n'nt. Ask$,a!' also insistihit the rot ronkni of c.rch bottlc should ercced 2.18m1. llis is moniiorecl by taking 5 br)ttlds cv.'ry h.rlf-hour from the en.l of the bottlingline and nrc.rsurnlg thc conteni.

(a) Describc holv you would dcmonsfratc b thc custoncr, Askrva\t thdtthe botiling proress l^,as stable.

(b) Describe hot' l'ou woulcl demo'rstrak' k) ih(: cusk)mcr thai thc boi-tling process rvas capable of meciing thc spccilicaibn.

sI0iher types oi c0nlrol charts i0f !arrables l9 l

t ) Lf 1ou1\ 'erc askrcl to ( temonsh'r t t the st . lb i l i l f and (aP:rbi l l f ' o i thenixins proccss hor 't{ oLrld rour nnnlvsjs differ fronr that dcscrlbedin paris ( i ) .nd (b).

Solution( . r ) Using d.r i . r compris i f t j f i \c bottk \ ' ( i lunrcs t . rkr ' r r ( ' !er l h. l i -hol l r

hnr s.rr .10 hoLrfs l( i ) calcul . r te mcin . , rd r ing! o i . i .h g(rr f o l5,

( i i ) . . r lcrLl . r le o\ f r . r l l mo.rn(X)r ,L l m(!rr r . r .se(R);

( i i i ) .n lculnte d R/, / , , ;

( i \ ) cnlc! l . r t t ' , r f t i (D.rnd h,rming !r lu.s h ' r r l r i 'nf nn(1 r ingc. l r r r ts;(v) Plot nrc.rns (nr Dt l , r .hn in{ l f i r rscs (nr r . r r rg( 'chirr ,(v i ) rssfss sLrbl l r iv o l f ( ) . .ss l f i )nr i | l h l ( ) .hn' ls

' rsLnl r . i io"

l i f .s , $ l r rn lng I n.s r f ( l srrPl) lemi '1. 'n 11'L( \(b) L ls i r rg i | l , ! ln l i r f ( inr t r r t ( r ) :

( i ) r l rn\r n his l { )8trrnr;( i i ) usi fs , , l f ( i r r r . r Iu ln l , ' r .J l .Lr lJ i . th. : l rn(1l f ( ] (1. \ ' i r t iorr ( ,1

r l l : (10 \ o l r1nr.s;(r l i ) ( (Drfr( lh(s l .n( l . r f r l r l f \ i r l i (Ds. i l .u lnt( \ l r r i t , r r ls( i ) , r r r l ( l ) ) ,

. \ f h i r i Ig rn\ ' ( l iq.ret . rx i ts $rth t n ' t r r r . n) t l r ( .hnr ls i( i r ) . ( )nrPrr f t l r f .nt) ib i l i i \ oJ t l ! 1] f { ) . i ss t r i l l r l lx sP.. i l i . . r l i , ' r l( ! ) l ) is .uss t lx . r | rb i l i lv i f (1 i . . \ $ i lh lh. .usnnrk t , nrnI in| ] I Ief

.n. . t ( i t lk h is l ( ) l t nr r r r ( l lhc.hi f ls . (See( l r r t to l0)(() lh( { l r t i sh(\r l (1 bc t l { ) ln\ l ns.rn in, l rv i ( lLrr ls r l r . r r t . lhet P'1i Lnl{)

n rb Ll f i f ) t r ( )ut , : o l , sn\ , 1. ( lhLr f r ( fn 60.ons., r r t i \ . Lrnt .hcs $r)Lr l , lL,( ( lcs i f , rb[ . ) N4er. nn{] f r rge .hrf is shorrL, l t , f f l ( ) t t ( \ l . rs in | r f t( . r ) . A his loBfrrr should bc ( l r rwn rs in f i r l (b) . l | l ' l lJpr(4rr i i t ( '!npnl) i l i lY rnJLVsis (( , ! ( l lh, 'n l ) f ( r t t i r (1 t r r l

!gX zls Stat st ca process contror

Shc(h.rr t . l ! .A. ( l9 l l ) l , r r , r r r . ar l r r r1 l . t er0/ ih/' l r ,J,J/ / , , .1|rd f tu, / , r . r . \ ' . , , , No!r f , i j iJ { l ( , t r )L ishrLl rn

l tr tht \rtnlDiil! .fles( l l ) \ AsQC Qlr l r | l

l I r l isnrr , / i r r l t St , i r rn i , , / l l . . .s :l \ .ss, \ l i \ iuk(, Wl, USA.I

l \hrc l . r ) l . .n( l ( h i f rb. fs. l )5 1l ! ! r2 jI nr l r ' t , lnd L1l i , S , ( 1, t r \ \ , Nrr) \ \ i lk , , f \ ,

s, Discussion quesl ions| ( . r ) T ' r { r , \ \ . ( r ) l ro l {h,r f t5 I r . r r b( . ( nss t t \ t ur t r l f f tw, j br(D( l h, . r ( l

r ' rgc, ' ! i f inL) l .s ' . rn( l ' . r r i f hrLres' . ( ( )nr l , r f r th{ ,s( . t r ! , ) ( . r t .1tr . i ( \, ' f ( l i f (1 i . . r l ( , h l r ( . f e.r l r (n i ' , r i (Nl . r t f r ( i f r i , j l ( .

(b) I r r lh , (n i t r , \ t ( i i i tL.r l i l \ . , i r l , ( i l . \ f t . ln t r t r , j l rs rrc. I r l t \ i , r r r l1 ' , r , ,1, /11,1 / r r5 ( , r i , ) , l r , r f l

I l i \ f l r i f l l r r r l i l l .n, f ( . , 1\ ' i$Mr , ! i

' I lvr i l ( , ld! f l i r r ( ) f1r l . r . t ( i f thr t , ( ) l r , rh i t i l \ ( ) l otr t , r in i , r ! , ( l ( ,1,r l i \ . !r ' , ' s inr f c (n \ rzt , , , ( l r . ' r \ | l r l r i r t \ r f | l , j l i ( f r fRj |or l i ( ! r l , ( tctr \ l iv .( i ) lh( . L, i r i { )nr i , r ( l is t , l t ) | l i t r r ;

(L i ) lh( l l ) i :s()n Ll is l , i l 'u t i t ! l. r / \ t , t r1, , r \ r l r ls lh,r l , , , j , r \ ( r , r1t . :0fr

. {J, l ( ) t r t r , t r ( , t15t , r r r t1r( . ( l l , r . rf r , r (hLir ' . r . ( l ( , j ( r . j j \ f l ) { l ( ,d, i r j . t t t l ) , ( ) l , . r t r i t i t ! lh,r l ( )Lr t , , t lL,r) t t l( | lN,r . r l I r I r l ( )nr :( , r ) l , 11,) (1, ( . ) l l r j ror l l lJ( j l ts$i l l l !J( , j ,1. i i \ .

5 lhr 'h ' l | ( ,s i r r r : reLorJslr tn\sr l r , r rLrnrtr( , r o l (1( . tcr l i \ . t i ( ,Dst()ur11 i f, ' s , rnr f , . { ,1 l ( l1 l l . r len ls. iLr 'per ( l , r \

SamDle number Number oldeleclives

Sample number

t l

13

t5

tb1718

2A

Number oldelecl ives

.ll21

l034

l

.l45

618I

t0

l

.l3

63Il5

lor j ! r ! r l l , r r r l rL rLj 211rs

Sample numher Nomber oldelecl ives

Number ol SamDle numberdefecl ives

i l l

l i l lI

.n)

I

I

I0

ll

III

1i l

I

\ , 1Lr l ' , r ' l l r , \ \ r . Jr i , t r . i f . l i ( ,1 Ll ! r l ! ' \ , L l , r l , i , r rL l L, , f r r ( . i ! ( ,1

1' l t ! . r i , ( l r . r l , ( . r ! , l ) \ ( Lr l .LLir i L IL- l l t , r I )l \ \ , r l \ : , i r i l ,LL\ , , i tLr l r , l \L (1lr , i I L) . r r rL l , t i iLr !1. . . r ( . . ( ( . ( !I r . . i , i , , t , . i , \L , , , t . :

I ) , : , ! r , , , , . ,1,1, , , , t ' , i , r . ( , , ,1,L, l t , , i' L) l I r ( \L \ , r l r L\ ( ) f 11, . L , , i ,1 . , i ( l i i lL , t . . i l l i , r ' .1, L '

( , r \L r i r l ln l , r l , l ( , 1! i ) \ \ , r ( , I r ( r r \u l l ! , ) | l l ! , , ! t \ ! 1, , , , r i , I n i r\ , r l , r ! L: l t , \ r , r l ( l rL\ , i r i (1:r i r l l r I r ( I ( r I , r1|( , I r

i l , r ! ) r f l No

l t t i t

l ! 2u

t tu l ! { l23t . t0 l

l l l , l i r l l r l i ,2, ' i1 l r l

I

t t 3 Mit03t! l

' r tL l t : , t i t t ]uS.t i l i l it i l l t9 21r 21 i l

l l l l1 l I

t l ): ,2

I

l5L

: t !!

xI 220 Stat istrca/ Process Control

Sei up a control chaft to monitor thc nlrmber of.:tefects. Whrt is iheaveraSc run tcngth to dctecrbn \arhen 6 defcts .re prcseni?f lor r \ , , , . i1, , , r t l -p, l ,Jr t . rn. l . , r rm,,r I up^r th- f . , , , . . .rqee.r i - . ( l r . r f r , r o D.- . r*r . , f tue-.r , ,n218 Aconirolclurt f()r.1nc\! kincl of plasti( is to L1c i,itiatr,.l. Trventv-fi\..,samplcs of 100 plastic shects from thc asscmbty line iverc nrsp;ctcclfor l l . { ,s dur ing a pibr rLrn. The rcsults.rrc givcn bctor{, . S{,r Lrp.rnappr('pn.ltc control chart.

Sample NoNumber oi llaws/sheelSample No.Number oi flaws/sheelSample No.Number ol flaws/shee1

1232309 10 11583

18 r9 20410

456242

12 13 14523

21 22 23324

7884

15 16 t7123

24 2521

In jury d atal . , r , I . , r t t . , i r , r .n \ , . , . , t , t ! . r , , t ) , i r 1,r . , , , r . . , , , {n1, . , . r } .1, \ r i , . . r t , , . l . ll l r r ' , . r ' r1 . . ' l I i r . r i , , . l , t r , . l I rn, l t . . t . rht , . | , | . | | . , I . | . | . \ l , l r , , \ i i r . r t , l )ih(srm( nnr(rnl ofh,n,rs tr(y( ' {1, t( , ( l ( ,n.h,,k,rrh 1.he i , rbl . , b"t , , , ;.oni.rins th( rlnt.r .oll{ cled (tr (,r.l 2-!c.rr p(,fnJcl

II Worked examples

Year I lllonlh Numbar ol iniuries (c) year 2 lllonth Number ot ini[ries (c]

Jatuary

l\jlarch

JLrneJuy

September0ctober

December

January

I\,larchAPr I

Juv

September0clober

December

62485

23T35

12J

t05I4322l343I

Use an .ppropriate ch.ritng nreihod to .1n.t|se thc datr.

bProress co l ro br ai t f ,br les 221 X

Sol!tionAsthrs.nr. Iu bfrof horrsr ' (Jf srr lcdf . r .h rn(Dth. i , .h i sh(nr l ( lhr Lr l i l iT. . l

) - , 1} .

l :n)rr lh.sc ( l . l i . lh, r \ , r rS. rur f lJr t , ,1 rniLrf ! ( s f . r rn.nt l r ( , Lrrr \ ' l t

l i l t r r '6s s l r ( { \ ! l l ( r , i , r t , ( ) l .h,rr l l r l rL \ \ i ! i r l , lh r ' l ( i r l in l l ( i i l ln i r f l t .s r .sul l l \ l i , i , , | ( ) , r l , rh( \ ( lh L( l l l ! f " i l t r lhL, , rLrs( \ , 'c , lr f r t r f r ) r r l ( ) i l r , l i ( l r \ l , r r \ ( l rk ' r t Jrrr i , ,S I l r , r r . r ( ! rL l r L l r r l f , r i r r ( \ i

| ,1, | l ( . f \ l . \ (L ssr\( ( i \ ( ,1 In( $. t rLs(\ l l . , t r l r ( \ . Lh| n( i rn.r l r r ( r | ' | l, ,1 h1,! fs$, , r1(1lr(rrnr() , t l i lh(r 'nrr . ' ls( i . ' r r r

' ( ,1 r i , , r ' l 'n l \ , r , 'n jh

t l

l l r . ( ( , , i ln, l l lnr l : r r . , rs i ( ) l l ( i r ' \ :

l \ l \ i - - l

t , \T l l r , l f t r r f n s ( l l r ( r . i s , i , i | . \ l lL\ \ l 1 l l ! l I : \ i : ' ,1 l \ i551 l015,,n( l l l t r ' !

16

Fiode8.8 . N[x ot r r ]L rr i r l l

\ - ,

at ! : i : j5 " ; i i =; i ;1 i' ; t : i 'P - . i6 i ;ct-

!

a

upptir warnrns ne

xf, 222 Slal s l ca Process Conlroi

bclow ihe contrc l ine st . l r t ing in Aprt l \ tar 2. Ih is indicated ihai the nvcr-.rg. numberot rcporte(t first'riLl casr.spcr nrcnth had heen red!ced. risr..ir'.tion $..rs .r tirjbL rte(t k) a srriich fronr s irc to |rlasric bnskcts for thc..1rr\ ing an.t storing .rf pnrt5 ind tool5 $,hich gre.jrtv rcdLrcod rhe nLrmLjcr ot injLrrics d& k) cuts. ll thls tr.fd .ontinlcs, thi. contrr)l limfts\hould b0 rc. . lk u lnted r hr f sUff ic icJrt dnLr rvcrc a\ , . r iLrbtc.

SoLr)

Herbic ide add i t ionsTh..r . t l \ f i r rgf t i i .nt in r l ( r t ic ido pro( luct is . r r l ( t .d in h\r) s l igcs. Art l r . l i fs t st . r i :c l6( l l i l ( s of thc i . i i \ ( ' rngr.( t t r , I t is .111(t(d r i ) 800 t i t fcs of thcIhd ingr( \ l i fnt . 1,r gcl r nr i \ | . t i ( ) of .x,rct l r : io I snrn qLr,rnirr ics () i. j lhr f in i j r .d icf l i |1 ' lh.n id, lcd. Ih is. . rn t )c \ . rv r i r ] r . .or ls lnr i r rg.rss( inxirnr(s I l , r fg( nL| |b.r ( ) l ndr l i r ions.rc rn.(1. Ln n . r i i ( ,nrpt h) g.rlh. f . r l ( , jusi r i l th l Ihc n\ fn i l r . rpf{) int( \1 I )u l | . t ion N, l . rn i { r r hrsInlr \ lLr .er l . r ru\ l )11\r \ lur ' l , i r thf l l fsrnr i \ i | !s l , i l l , t i ) t ,s l lh.cf i ( \ rr ! r ,nt ss ( , t th is.h.rngc hf re.() fdr \ l i | l ,nInrLro .1 , r ( t ( i r t i r r rs R\ l I i rc( t l ( !l1) . , r \c.ui i \ | b.r t .hcs, l5 s i lh l l r . (n, l Pro.cr lur , . rn, t t5 wi th thc ru! .l r i r t r r ' ( st) is brs.r l or t l j .s , ( l , r l . j :

( r )

(h)

WlI i . (nr ]Lrs i ( r rs [ { ,Lr l ( l \ ( \ rJ i rw 1|1r]r t t r , . (n l , ( ) l . t r , r in I , i i luR, l i r r ,r fgrrd Lrr l t the nctr f r r r1 l ! r .?l \phirr htr \ lhr p()s i l i (D ot t l r ' ( ( ! r l , l , l r r r l r f i I r i IB l in( ,s werc r i l.u l r l { \ l l { ) f I igur( S.e.

Io

bt"

510 15 20 25

f iqure 0.9 N!hber oladdlons req! Ed ror 30coN(l tNc batches orhtrb.rde

xI

:1.r Ih is

PfocPr5 conirol by al l rbrrPs 221

So ut on(a) This is i . chart ,bnscd (n1 thePoissondistr ib l rL ion. ihcc(,nhct jneis

dr. t rJr . t :1, I 'h ich is th. mein for th. ' f i rsr 15 point ' UAL is.r t' l + 1, ,1. No lor | r r ic i io. l ine has brcn drr$ n. ( .1 3, .1, $,oul( t b. ,nrg. t i !e; a Poissor l lv i th a I would bc rathcr skclvcd ) Thir iecnof the Llst l5 poi f ts.rr . l or b. ' lo\r thc (cf t re l inc. l h is is st fong c, \ idcnce of . df . r . ls . b l r t nr lght not bc n( i t iccd b) sonreone usingf ig id ru] . 's . A .u\unr rhn( nr.r \ bc us. f l hfrc ls$ Ch.rptcr cr ,lV(trkcd cx.rnrplc 1).

(b) B.sed on lhe I1, is{n distr ibul on:

, ' r rJ: i r G to., ' , : ,F + r :J i s.

UAIL \'\' I

g!

! .1!rs l ic b. lotr ihc t . r f { f t \ r lLrr : ( .hf I t lx , l ( f o i thc,u{rnr tL, , r( l rnrrgcs t l r f rnr : r fvrd \ r lu.s. f ( , .h,r f { i r ) i :' I l \ ' .us!n i i \ hn r l1|( . . | ) b. Lrn\ l io i , r l t , rL)Lr( \ , r f ,1 \ . r r i . r lJ l f . h\ t rd. l rnnir ins lh( , s. . r l , . lor f l ) l l l r r i t lh( . lx \ \ i I i t th.l i fg( , r \ . Lr( , . 'n( l v l fL !1, , j L. \ ' ( i i : l (J l r . , (L)rr(* l (nr l r j jg rr , fn\ l t .' ( f lnI i . ( r { n,rn1}slh, ,L,elr . rvor i ,J l

. r t r ( \ . ! . L, in ht . ( , , , , i t ' r . lk r ( \ t . \ r lcrr t . , r t t , rr \ I rg i l r f Sh(,sh,rnnr iJ(u\Un)(hl l \ i r i ( r )nr l , r , r t i ( , r i l l ! ,Sh\! l r , j r r.h i r lsrr f l r ( \ l r \ \ l . ,1 l l r ( , l \ inL , ,1 ( t f r t , , , l ,s l l l \ t t r ( . t L i i r I r ( } , r f ] \I l l .n,r l l ( i r , r , ' l ( i r \ rcn i ) l r l . r l , lsh\ \ l i .1r l r l r , r ' i \ r fc , , , . r , \ ( r \ i1 \ ( . t , , rJI i ( l f l r r r j { , \ nr l l r i r jf f , !1. :s.$l ' c l I r , , I r \ r | , , i i . I I I ( i I , qrrr \ I \ , . | ( j I I I t | ( . iL\ I i ( j I I t , : I j j , | | |susr. ' r ' r ( \ r . f , ' i r r t .s\ : r i ( 'LrsLl( \ ls l ( f , t , , ( \ . (1rr( \ l , , f l l i ( r1. , | t r , t , r1 i ( ,n( , r , !s!r j j f1, , t . . , ,1.l r$ i l r l t r r '1, t l i , rS t l i ( , q( ( i l Y, , i , r , .1. ,l l ,L ( t t rq l r r . l i , i , , , ,1 l l r ' \ ' r r r r , l i \ ,Lr . r l l r h,r ! r ( j I L l r n, l jL l . r l, , , ( i r ( i i L l r t . l i l ( ) l r , r l \ . r , I I , L . I i , t I i , I I i | , L I I | ( j I j r | ( l i l r , . , \ t t t t , i , f ( . r r r ( - .l l ! r r (Fl Ni( l , l \ L, \ \ l Y nr,r \ t l j , r \ ( l . r r . r ( ! r r r - . : : f l , j i . . j r j j t ) t , ,/ . r ( i l0Sl , r l , , r i i , l ) l f lL l

Helerences and lurther readingl i . i r r r t l . ( ,11ei , r l ' l ) r \ i ! r ) l rLL.r \ r l \ i . i . . , r , f 1. . ( i r i ( | , r \1. \ j j( r r r . . 1r t ' l r , / lnrrr . r r . ! , ,

.1, i lr ) f rnf . , \ l 1 l , , f6r ( ) | i r l i r r ( , ! / r r l l I t l l , " l ! t t ) t l ! r r r r r i , . . , j l r lLt r t rsL0,

L l , r r i , .n tn!1, l l . I S \( , r i r t , , l i \ l t l ! r r ) : ) 1/ i t r , / , l r r r / . r r : \ .1 l , | ' , , I l , rn, , , r ,LIrLr.r \ ,

. ,LLfr ! , , ' . . r r I t . l |11 i | \ tnr l r ) , . ( l r ' | ( . .

I urscusst0n quesl lons( , , ) | \ l ' , r r r ) lh, l rLn. i t , lL s in Slr( \ \ h,r i ( (D1,,) ( l i r f t \ { i ! \ , I i r ln( . r i r , . . i .

, ' r t l s . ' rn l l ( , , , , , ! ( . , r f ( l LLrr i , l , i l \ . , , ! I ( ( r r l r i l ( l r , j ,1. . l ( j f : , rnr t j , .r ' r (N. Jn( l : , i , ' r f l . r , ' r ' f l ( ( ! l | . , . t lk l ! , r l t ' r r r , l r ( . ( i i I r \ . L | i , , , l \( t ' ) \ , hrrr , l , L. , j r . ) rL l . r ( l rLn I i ,L[ . \ , r \ [ ) r l )1, . ( j j \ \ l ] ( ) \ { \ , r l ih, . , . j ( l( ) i ( , , ! h h( j ' , r i f ( ) r ( l . f I ( ) \ , . f r \ l l t r r . i l l r t L) t lh. L t j ( ! , ) t , r l ( \ , ( r jt . ' i f ( ! l r i lh i . f . r l r l r { ' \ lh nLi \ i ( lL.r l r l ! t r ( i l , r l t \ . , , . . r1\)( . \ . i f irx\ l \ is | , r l l \ ( lLr f i i t t l r ' ( | l ! | . \ r g l r i r rq. | rLI lh. \ . r i ( )us l \ f ( .s ( j

r r ' , i I ( ' f , rn( l f r inof l , r rL l t : . I . ( (JL,nlr lI l r ( r r r f rL l , r f { r , . r er l rL,r l ( \ L nr.r l ( ) f r . r r l t l ( ) I I r lnt , r l . rLLl t \ . | r l , r ( \ r . f rs

.r r r . r \ inrr nr rqui \n l r r r l to I f r in( i r t l r \ \ t r . r1 l . r { r l r , , rh( \o l , r l t , . n.rrr \t ) ( i \ l . r ( ' l i Lro\ ( ( ! r l r i .s I I .ho.() . rh s.I ) is( Lrs\ how thc ( u\ ! rn r h i r l tc. l r r ) i ( tu. , . r . br , I i r ( l n) r i r (nr i t , i r lhIt l rVsi . i l ( lc l ( . ls J l lu+r.r l { h( t r \ lhr .hnrt s l r lL l bc $t ! l ) . r ( l U\oJ

&I 242 Starrst ical Process l ]ontro

In the tablc bclo ale givn th.'rcsults from.. r rJr- t . , r

-

j r .LF.. , , , , , r , . i r ,k. , l r r runsthe inspectior of filing

Cabinet No.Number ot defeclsCabrnel NoNurnber of delectsCab nel NoNumber ol defects

123103I 10 11

l0 I 4l7 18 194t l

4563

12 133T

2A 2l10

6734

14 1553

22 2345

I5

l6l

24 2555

3

Ploi tho cl . rhr on ,r sLr iLrhly designcLl f l rsL|rn.n.fr ( lnd commcnt of(s|( ' n so C h.pt( ' r 8, Dis.ussion qucsrn)n 7)I hf n) l lotr ing rrcor{ s ln)r 's t lx nrnrtrcr () f J(t .cr i ,vf i t ( rns foon. l ini s.rnrpLc 1,f 100 i . rkcn ts, i . r pfr dnl .

Sample number Number olde,eclives

l23

56l8I

t0l t12l3t415t611

t920

3263

l5

4l2l

l03

21222324252627282930313233

3536373839

2l03

0l30J02ll40232l

Sci Lrp ancl plot a cusum chart. lnkrpret your findnrijs. (Asslrnle irtarget r'.rlue of 2 d('fectives.){s.c also Chaptcr 8, Discussion qLrestion 5)

Number oldeleclives

Samplenum0er

XIl ]umulatrve sum {cusum) charts 243

The tablebelo' givesihearerateh' idth( 'nm) forc.r .h ( , f 20 samplesof five panels. Also given is ihe rante (mm) of each sanpk.

Sample number Mean Raflge Sample number Mean Bange

: '

?a

I23

56T8I

10

42426741325807599519

t l1213t415tb17]Ul92A

550.8552.7553.9555.8553.8

550.9552.0553.7557.3

553 r 3.8551 7 3.15612 35554 2 345523 585529 l6562 9 2T559 4 5.4555 8 1.75476 67

I ) ( s i l i f ( unrul . r t i \ ( sunr (cusunr) .h. f ts l ( ) . ,Dtfol lh( Pf{Jccss I \p ln lnth. { l i t t r | ' ( ' ( r 's b. twcfn lh( s. .hr s ind Sh( ' t r h.r f t fh.rr ts lor r r renns

(s|c r ls(r ( h ip i ( . f 6, l ) is .L1ssi ,n qr(s l r )n L0)Shf\ ! h i f l .h i f ts r fe t (J Lrf Lrscd lo nr.r in ln in . (nt f ( ,1 on r l issol ! .d i f ( r r.ont( ! r t ( t i ( lvcsluf i l { rnrr1l . r l r , r i f l , r r l \ p( r nr i l l i ( , r r ( fprr) Alk r 25sr lb l t f ( r rPs ( i i 5 m .rsLrf , n l ( ! r ts h.r ! . b,{ n (nr l . r1nc!1,

wh( t r , i , . nx!n of i lh srbgr(rrP;R ., rnng( of iih suLrgn)Lrt,

L)(s ign npPfoPrirk ( uslrnr (hi r ts l , ) r . (nr i r ( r lo l lhc p.(r t 'ss nrean andsimpl. r ingc Ind d( scr ibc hoN ihc chnfts nr ighi | ) | usrd in cont inuoLrs pr(x luct ion f ( ' r producl scrccning(s('

.lso Ch.rpl0r 6, l\'orked i'\inrpl(' 2)Th( ' fo l lowifg d. ta \ r 'crr obtninrd whcf mensurrm. 'nts w. ' fe mi. [on the di.nr('ler oi sici, balls foftrsc Ln beirifgs. Thc mean rnLt f.n1sc\ ' . lu( 's oi s i \ t f ( 'n s.nrpk's of s izc 5 . ] f r l t iven i f ihf tablc:

Sample Mean dia. Samplen[mber (0.001 mm) ranqe (mm)

Sample lvlean dia. Samplenumber (0.001mm) ranqe (mm)

254 2 0 0050 005

250.4250.0

It0

0.0040.004

(Conl inued)

r J l 51 r f r ! , r .

Sam0le lv lean dia. Samptenun0er (0.001mm) range (mm)

Sample Mean dja. SamFtenumber (0.001 mm) ranqe (mm)

\I5

!

l

t1

2511 l

21l l u

1t oul1l1t0l l{r u011l0t) tf) !051r oul

t . ] l t . l:)1U rJ2,t l l . i2.1! |251 t)251t rl

1) 001!0 fr0t5(t lt0,ll0 0trirl| 00-r0 t)1t rl

Lt

u

L]l iI

( ;uI

( l

l ) ( - . g,r , r j I t . . , , r ( L i . . r | ( lL,r l t ( , , t t r ( .1, , t \ ( \ . . , r , rLt i r t , j l i l r ( . r , : r r \ r , I i j , .l , i lL, t , r ( . t l ,L (Lr. . r , I t i , rL. I r t ( . \ f l , I t ) r , . j r \ hL, \ \ r t , j r . r \ hL.L, !L\ l l , jL) l \ L, l I i r . \ i r i l t . .

: Nl , l i l . i i r ' l \ , r ( . i ( i ,nr t , , , j \ ( t i . .L r , r !L\ L. t I ( , I t . , r j j r , r ! ,1\ . r r t . l ( . , rr !1rr $oir \ , I r I I L j I I I ( , I i r \ ( , I Nl l tLt t , l I L i , ' \ , r : j l r f j t t . ( ) ( t \ . ) , j r1t . i . .

l , j rLr j , r i rL l , r r , j l \ ! \ l t I I I I , L ( | r I i I j ( . i I I I . , I j r ! | r (o t r r i t i t - ,L i t t . , t I I r ll l ! ,1, ' i l \ . . , , , ) j I lL ' . . t { ( . , r tL l ( t , j \ l ! . r , \ . l ( j t j \ , , I j r Ltr . l , r l j .

Dav Am onia (ppD)

2i t l ll i2 l L)

:2|2.1t)

2i . l2t lt2t l i l299

Tempeialure l 'C)

I I

l

t ,

'1

t : )

!l

i

0peralor

I

.l5( i

N1l

i l

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1lti

cumu at ve sum (cusum) char ls 245xI

Ammonia contef t (Con