49 th European Organization for Quality Congress Topic: Quality improvement. SPC in Short Production Runs with Autocorrelated Data

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1 49 th Euoean Oganization fo Quality Congess Toic: Quality imovement SPC in Shot Poduction Runs with Autocoelated Data José F. Gomes Requeio, Ana Vilela atos and Zulema oes Peeia Deatment of echanical and Industial Engineeing, Faculty of Sciences and Technology, Univesidade Nova de isboa, Quinta da Toe, CAPARICA, Potugal. ASTRACT The statistical ocess contol alied to industial systems with a geat divesity of oducts/chaacteistics esents a few imlementation difficulties, since the taditional techniques wee conceived fo lage volumes of oduction. The difficulty inceases when the quality chaacteistics exhibit significant autocoelated data. In this aticle a methodology is esented to ovecome these oblems. In the fist stage of SPC, called etosective analysis, the methodology contemlates the use of the auto-egessive integated moving aveage (ARIA) methodology to model the ocess elated to each of the quality chaacteistics. Aftewads, the Shewhat contol chats ae alied to the obtained esiduals to veify the ocess stability and the caability analysis is efomed by using the taditional C and C indices. Duing the second hase, the so-called ocess monitoing, the statistical ocess contol in eal time is caied out though standadised contol chats alied to the foecast eos of all the oducts/chaacteistics. The ocess caability is analysed by estimating two caability indices Z and Z, suggested by the authos of the esent aticle, which ae detemined at each instant consideing the estimated values of the ocess aveage and vaiance. The esults show that the aoach eveals a few advantages as seveal oducts and chaacteistics can be contolled by the same chat. Simultaneously, since the autocoelation is eliminated, the ocess aametes estimates ae moe eliable. Additionally, the oosed eal-time indices constitute a good altenative to the taditional C index. INTRODUCTION Significant advances have been ublished on SPC since the contol chats wee fist develoed by Shewhat. The taditional chats, nown as Shewhat contol chats, esent limitations to detect small and modeate shifts in ocess aametes. This insensitivity to detect was solved by the intoduction of the uns ules, fistly esented by the Westen Electic (956). These ules incease the sensitivity of the classic contol chats to detect secial causes of vaiation, which is desiable, but, on the othe hand, they also incease the is of false alams. To solve the oblem, i.e., incease the sensitivity in detecting secial causes of vaiation without inceasing the α value, Page (954) intoduced the Cumulative Sum (CUSU) contol chats, and Robets (959) oosed the Exonentially Weighted oving Aveage (EWA) chats. The CUSU and EWA chats ae concetually diffeent fom those of Shewhat s, since each oint of the gah efes to a moving aveage of the statistics values, whilst that in the classic chats only indicates the instant value of the U

2 statistics. Seveal authos esent develoments of the CUSU chats, both fo ocess mean and disesion contol (e.g. ucas, 976, 98, 985; Hawins, 98; Gan, 99; Chang and Gan, 995). Equally, thee have been many develoments in the EWA chats (e.g. Cowde, 989; ucas and Saccucci, 99; acgego and Hais, 993; Gan, 995, 997). Cetain assumtions, such as the data indeendence and the distibution s Nomality, must be taen into account befoe alying the above contol chats (Shewhat, CUSU and EWA). We suggest the use of the Kolmogoov-Sminov test to veify the Nomality, and the detemination of both the EACF (Estimated Autocoelation Function) and the EPACF (Estimated Patial Autocoelation Function) to identify the existence of autocoelation in the ocess. Anothe limitation of classic contol chats is the difficulty of alying them when thee ae seveal oducts/quality chaacteistics unde obsevation. This subect has been studied by many eseaches in the field, such as othe (988), Giffith (989), Wheele (99), Pyzde (99), Quesenbey (997), Peeia and Requeio () and ontgomey (), among othes. As a esult, moe tools have been develoed in ecent yeas; examles ae, fo instance, the Diffeence contol chats and the Z and W nondimensional chats, which ae modifications of Shewhat s chats. These new statistical contol tools ae best suited fo shot oduction uns, when is ossible to estimate the aametes of seveal ocesses. Othewise, when data is not sufficient to estimate the ocess aametes, Quesenbey (997) suggests the use of Q contol chats. None of the above mentioned techniques can be diectly alied to the selected statistics when dealing with autocoelated ocesses. A suitable aoach fo solving the oblem consists in finding the mathematical model that best suits the data, and then aly the contol chats (Shewhat, Z and W o CUSU and EWA) to the esiduals o the ediction eos. The statistical ocess contol with autocoelated data has also been a matte of concen fo seveal eseaches, with aticula elevance fo Alwan and Robets (988). Among othes, one can also cite Alwan (99), astangelo and ontgomey (995), in and Adams (996), u and Reynolds (999), English et al. () and Timme, Pignatiello and ongnece (-). This ae esents an aoach to deal with autocoelated data in shot oduction uns when thee is sufficient data to estimate the ocess aametes. The aoach is alied to a case study to contol one quality chaacteistic that is common to seveal simila oducts. SPC WITH AUTOCORREATED DATA: APPICATION TO SEVERA PRODUCTS The use of standadised contol chats is suggested to contol seveal oducts/quality chaacteistics. The alication of standadised contol chats, nown by Z and W, is ecommended when sufficient data is available to estimate the ocess aametes. The methodology oosed by the authos consides SPC s Phases and.

3 Phase coves the etosective study of the ocesses and has thee main goals: the stability veification (inexistence of secial causes of vaiation), the ocesses aametes estimation (cental tendency and disesion) and the caability analysis. Phase concens the ocess monitoing and allows the detection, in eal time, of secial causes of vaiation. This facilitates the investigation of the oot cause of the oblem, as well as the timely imlementation of coective action. Phase Duing this hase, the classic SPC chats ae alied to each oduct/quality chaacteistic. The ocedue should tae into account whethe, o not, thee is significant autocoelation in each ocess. Fo ocesses with indeendent data, the Shewhat chats ae alied diectly to the quality chaacteistic unde study, tyically using the,, s, R and R (moving ange) statistics. As mentioned befoe, the data indeendence is veified though the detemination of EACF and EPACF. In contast, fo ocesses with autocoelated data, one should adot the following ocedue: Ste Comute the EACF and the EPACF fo the data of the quality chaacteistic. -The set of coelation coefficients ρ, fo,,,, is called Autocoelation Function (ACF). The autocoelation of lag is the coelation between any two obsevations lagging eiods. The ACF must be estimated though the values of the andom vaiable. ox, Jenins and Reinsel (994) conside as the best estimato fo ρ : ρ (, ) Cov t Va( ) t+ N γ t ˆ N γ γ ( )( ) t ( t ) t t+ γˆ ρ ˆ () In the evious equations, the following notation is adoted: Cov ( t, t + ) covaiance of obsevations that ae eiods aat Va ( ) vaiance of auto-covaiance of lag γ γ auto-covaiance of lag, o vaiance of -The atial autocoelation of lag is defined as the coelation between t and t + without the intemediate obsevations ( t+, t+,..., t+ ) ; the atial autocoelation coefficient of lag is designated by. ()

4 -The set of autocoelation coefficients, fo,,, is called Patial Autocoelation Function (PACF). Since the coefficients ae unnown, they need to be estimated by elacing ρ with in equation K 3 (3). The..., ˆ, ˆ, ˆ 33 estimated values ae then obtained, constituting the so-called Estimated Patial Autocoelation Function (EPACF). The ae comuted as follows: K 3 (3) Ste Analyse the time seies to identify the best suited mathematical model, taing into consideation the EACF and the EPACF functions. Fo this uose, the authos suggest the use of ARIA (Autoegessive Integated oving Aveage) models develoed by ox, Jenins and Reinsel (994): ( ) ( ) t q t d ε Θ Φ (4) in which, ( ) ( ) Φ (5) ( ) ( ) q q q θ θ θ Θ (6) t t (7) t t t (8) whee: bacwad shift oeato bacwad diffeence oeato ( ) Φ autoegessive olynomial of ode ( ) q Θ moving aveage olynomial of ode q t obsevation in eiod t t ε white noise in eiod t ( ) ( ) ε ε,σ N ~ Ste 3 Detemine the time seies esiduals, based on the eviously identified ARIA (, d, q) model.

5 Ste 4 Veify if the EACF and the EPACF esiduals ae indeendent, i.e., without significant autocoelation. Ste 5 In the case of indeendent esiduals, chec thei distibution s Nomality. Ste 6 Aly the esiduals contol chats (Shewhat o CUSU and EWA). Table esents the contol limits fo Shewhat esiduals chats. Chat R Chat Chat s Chat Table Contol limits fo the esiduals chats Phase C C UC A R A R D 3 R R D 4 R A 3 s A 3 s 3 s s 4 s Residuals Chat 3R d 3R d R Chat D 3 R R D 4 R The evious table adots the following notation: C lowe contol limit C cental line UC ue contol limit R samle ange s samle standad deviation R moving ange R aveage of the samle anges s aveage of the samle standad deviations R aveage of the moving anges A, A 3, 3, 4, D 3, D 4, d constants that deend on the samle size n Ste 7 Estimate the autocoelated ocess aametes, E ( ) and Va ( ) equations (9) to (4): AR odels (Autoegessive) E ( ), fo each model, by using ξ µ (9)

6 Va ( ) γ σ ε ρ () A odels (oving Aveage) ( ) µ E () Va q θ ( ) σ, γ ε () ARA odels (ixed Autoegessive and oving Aveage) E ( ) Va ξ µ (3) ε q ε ε ( t ) γ θ γ ( ) θ γ ( q) γ + σ (4) These equations adot the following notation: σ ε white noise vaiance ξ aamete to calculate the ocess mean aamete of ode of the AR o ARA model θ aamete of ode of the A o ARA model ρ coelation coefficient of lag γ auto-covaiance of lag Ste 8 Analyse the ocess caability, using the taditional caability indices Phase C and C. In this hase of the SPC, the authos suggest the alication of a single chat fo contolling the ocess mean, and the use of anothe one fo contolling the ocess disesion. These two chats include evey oduct/quality chaacteistic. Fo this uose, the data is tansfomed, using the aametes values of each ocess estimated in Phase. Theefoe, the samle mean (o individual obsevation) obtained at instant i, fo each oduct/quality chaacteistic, is tansfomed into the ( Z i ) statistic. Similaly, the samle standad deviation (o ange, o moving ange) at instant i, fo oduct/chaacteistic, is tansfomed into the ( W statistic. ) i

7 Table shows the Z and W statistics fo vaious tyes of chats, as well as thei contol limits fo a significance level of α.7% when data is indeendent. Table Statistics and contol limits of Z and W contol chats Z Chat W R Chat W Z i i Tansfomation i µ d ni ( i ) Zˆ µˆ i ( σ ) R Ri ( µ R ) d ( Ri R ) ˆ ( σ R ) W Contol imits C C UC i d R 3 Z Chat W s Chat Z W i i s i i µ ( σ ) ( µ s ) ( σ s ) ( i ) c n ˆ 4 i µˆ i s Z Wˆ i ( s s ) c4 i s c 4 Z Chat W R Chat W i Z i i σ µ ( ) d ˆ i µˆ i Ri ( µ R ) d ( Ri R ) Wˆ i ( σ R ) d R Z R The notation used in Table is as follows: obsevation i fo oduct/quality chaacteistic i i samle mean i fo oduct/quality chaacteistic R samle ange i fo oduct/quality chaacteistic i R s i i moving ange i fo oduct/quality chaacteistic samle standad deviation i fo oduct/quality chaacteistic µ ocess mean fo oduct/quality chaacteistic

8 σ ( R ) ocess standad deviation fo oduct/quality chaacteistic µ mean of the samle anges distibution fo oduct/quality chaacteistic ( µ s ) mean of the samle standad deviations distibution fo oduct/quality chaacteistic ( µ R ) mean of the moving anges distibution fo oduct/quality chaacteistic µˆ estimated ocess mean fo oduct/quality chaacteistic R R s n i ( ) aveage of the samle anges fo oduct/quality chaacteistic aveage of the moving anges fo oduct/quality chaacteistic aveage of the samle standad deviations fo oduct/quality chaacteistic i samle size σ standad deviation of the samle mean distibution fo oduct/quality chaacteistic ( σ R ) standad deviation of the samle anges distibution fo oduct/quality chaacteistic ( σ R ) standad deviation of the moving anges distibution fo oduct/quality chaacteistic ( σ s ) standad deviation of the samle standad deviation distibution fo oduct/quality chaacteistic When ocess data is autocoelated, the Z and W statistics ae comuted fom the ediction eos. The ediction eo fo T + τ eiod can be defined by equation (5), i.e., if T is the actual eiod (it coincides with the latest time seies value of Phase ), the ediction eo fo the T + τ eiod is: e ( T ) ˆ ( T ) (5) τ T + τ T+ τ Accodingly, the ediction eo vaiance may be calculated though the white noise vaiance (ontgomey e Johnson, 996): τ ( ( )) + Va e τ T σ ε ψ (6) In equations (5) and (6): e τ T ediction eo fo T + τ eiod ( ) T +τ value fo T + τ eiod ˆ T ediction of fo T + τ eiod, caied out at eiod T T + τ ( ) Ψ ε : ψ coefficient calculated fom t ( ) t Ψ ( ) + ψ + ψ + ψ, and ψ Pediction eos ae indeendent and follow a Nomal distibution, with mean equal to zeo and vaiance given by equation (6). Theefoe, to calculate the Z and W statistics one can use the equations in Table, by maing the following elacements: - values ae elaced with ( ) T e τ

9 - µ ae elaced with zeo, and σ ae elaced with ( ) ( e ( T )) - EP ( Va τ ) σ. Unde these cicumstances, the Z and W contol limits ae -3 and 3, fo both indeendent and autocoelated data, as shown in Table. The ocess caability analysis is then caied out in eal time, using the standadised indices which ae defined fo the oduct/quality chaacteistic, in each instant, by Z and Z U, (( Z ) ) ( Z ) ) U IE µ σ SE µ σ (7) (8) whee: S lowe secification limit fo oduct/chaacteistic ( ) ( US ) ue secification limit fo oduct/chaacteistic (( ) ) Z lowe caability index, fo instant, and oduct/chaacteistic (( ) U ) ( µ ) ocess mean, fo instant, and oduct/chaacteistic Z ue caability index, fo instant, and oduct/chaacteistic ( σ ) ocess standad deviation, fo instant, and oduct/chaacteistic minimum value fo acceting a ocess as caable The values µ and σ fo oduct/chaacteistic, ae estimated using evious data fom Phase, and also data obtained duing Phase. When samles ae used, the estimated values fo µ and σ ae given by: ( ) + ),,, µ ˆ 3 (9) s ˆ σ (( ) s + s ),, 3, () c c 4 4 Similaly, in the case of individual obsevations, the estimated values fo ( ) + ),,, µ and σ ae detemined by: µ ˆ 3 () s ˆ σ s + ( ), 3, 4, () c c 4 4

10 CASE STUDY The case study deals with SPC alication to the density of five tyes of wate aints. Fo each aint, the density values of batches wee measued. The EACF and the EPACF wee comuted next to veify whethe any of these ocesses exhibited a significant autocoelation. It was obseved that aints 3 and 64 had significant autocoelation, whilst the othes wee indeendent. Figues and show the EACF and EPACF fo the density of aint 64. The softwae Statistica was used fo the mathematical modelling of the two ocesses in which autocoelation had been identified (i.e., aints 3 and 64). y comaing the EACF and EPACF ofiles with the ACF and PACF, it was ossible to ascetain that both ocesses fit the AR() model. Tables 3 and 4 dislay the esults of the estimated aametes. ag Co. S.E Autocoelation Function Density - PAINT 64 (Standad eos ae white-noise estimates) Figue EACF fo density of aint 64 Q

11 Patial Autocoelation Function Density - PAINT 64 (Standad eos assume AR ode of -) ag Co. S.E Figue EPACF fo density of aint 64 Table 3 AR() aametes fo density of aint 3 Paametes Standad 95% Confidence Inteval Deviation value owe limit Ue limit Constant Table 4 AR() aametes fo density of aint 64 Paametes Standad 95% Confidence Inteval Deviation value owe limit Ue limit Constant Afte modelling the two ocesses, the density esiduals wee calculated, and the coesonding EACF and EPACF wee analysed. The esiduals wee found to be indeendent in both cases. Figues 3 and 4 illustate the EACF and EPACF fo density esiduals of aint 64.

12 ag Co. S.E Autocoelation Function Density - PAINT 64 : ARIA (,,) esiduals (Standad eos ae white-noise estimates) Figue 3 EACF fo density esiduals of aint 64 Q Patial Autocoelation Function Density - PAINT 64 : ARIA (,,) esiduals (Standad eos assume AR ode of -) ag Co. S.E Figue 4 EPACF fo density esiduals of aint 64 The following ste alied the Shewhat and R chats to the data of the thee aints without significant autocoelation, as well as to the esiduals of aints 3 and 64. As mentioned eviously, the Statistica was used to constuct these chats.

13 Figue 5 illustates the contol chat of a aint in which the data was indeendent (aint 6), and Figue 6 shows the contol chat of a aint with autocoelation (aint 64) and oving R Chat Density - Paint 6 :.3698 (.3698); Sigma:.58 (.58); n Obsevation oving R:.94 (.94); Sigma:.9 (.9); n R Obsevation Figue 5 and R contol chat fo the density of aint 6 Residuals and oving R Chat Density (Residuals) - PAINT 64 : -.73E-4 (-.73E-4); Sigma:.994 (.994); n Obsevation oving R:. (.); Sigma:.847 (.847); n E R Obsevation. Figue 6 and R contol chat fo the density esiduals of aint 64.

14 The and R chats wee constucted again fo all aints afte emoving the secial causes of vaiation. This time, no secial causes of vaiation wee detected. Additionally, it was ascetained though the Kolmogoov-Sminov test that all distibutions (of data and esiduals) wee aoximately Nomal. As the ocesses wee unde statistical contol, thei aametes wee then estimated, as well as the caability indices, which values ae esented in Table 5. Fo the ocesses with indeendent data, the and R d estimatos wee used fo the mean and standad deviation esectively. In contast, fo the ocesses with autocoelated data, the estimatos ae those given by equations (9) and (). At this stage, Phase of SPC was comleted, as all ocesses wee stable and evealed satisfactoy/good caabilities egading thei technical secifications. Comaing the last two columns of Table 5, one veifies that the ocesses ae not efectly centeed; nonetheless, they ae centeed to a satisfactoy level. Table 5 Paametes estimates and caability indices Paint S US µˆ σˆ C C ( ) C ( C ) U The examle also coves the monitoing stage of the five aints ocesses, i.e., the SPC Phase, and the eal time analysis of thei caabilities, fo which the authos have used the caability indices Z and Z U oosed in this ae. To this uose, the density data of 4 consecutive batches was obtained fo all aints and, at a late stage, the data was tansfomed into Z and W statistics, using the equations esented in Table. The caability indices Z and Z wee calculated though equations (7) and (8) fo.33. U Figue 7 esents the Z and W contol chats, which illustate the efomance of these five ocesses. The figue shows a secial cause of vaiation in obsevation 39, concening the aint 64 density; this haens fo both the ocess mean and disesion. The oot cause of the oblem was identified, uon which coective actions wee imlemented. The authos highlight a aticulaity in the Z chat: due to the secial cause mentioned above, the Z and Z U indices should not be comuted fo obsevation 39.

15 Z Density - Z Chat Poduct / Obsevation Z C C UC Zl Zu Density - W Chat 3 W Poduct / Obsevation W C C UC Figue 7 Z and W contol chat fo the density of the five wate aints CONCUSIONS The alication of SPC to ocesses with autocoelated data deseves secial attention if one wishes to avoid incoect analysis. An eoneous aoach may lead to biased conclusions about the ocess efomance. The advese effect of ignoing the autocoelation may be manifested in seveal ways: - Accet as stable (i.e., unde statistical contol) a ocess that, in fact, has secial causes of vaiation. - Identify (false) secial causes of vaiation, when indeed the ocess is unde statistical contol. - Estimate incoectly the ocess aametes. - Given the lac of ecision on the ocess aametes estimation, one may eoneously accet o eect a caable ocess. Thee ae imotant advantages in using the Z and W chats in the contol of seveal oducts/quality chaacteistics, and also in using the Z and Z U caability indices, namely: - Ability of contolling all oducts/quality chaacteistics in the same chat.

16 - Analyse diffeent chaacteistics in the same document (chat). - ess time consuming analysis. - Real time analysis of ocesses caability, which facilitates timely coective action. In site of the advantages highlighted above, thee is also a limitation, which is the difficulty in identifying non-andom attens fo each oduct/quality chaacteistic. This fact inceases the comlexity of the analysis ootionally to the numbe of vaiables. Finally, it is stessed that detecting secial causes of vaiation and imlementing the subsequent coective actions educe the ocess disesion, which is an imotant contibution to the quality imovement of ocesses and oganisations. IIOGRAPHY Alwan,. C. (99). "Autocoelation: Fixed Vesus Vaiable Contol imits", Quality Engineeing, Vol. 4, Alwan,. C. and Robets, H. V. (988). "Time-Seies odelling fo Statistical Pocess Contol", Jounal of usiness & Economic Statistics, Vol. 6, othe, D.R.(988). SPC fo Shot Poduction Runs, Intenational Quality Institute, Nothville. ox, G. E. P., Jenins, G.. and Reinsel, G. C. (994). Time Seies Analysis, Foecasting and Contol, 3. th Edition, Pentice-Hall, Englewood Clifs, New Jesey. Chang, T. C. and Gan, F. F. (995). "A Cumulative Sum Contol Chat fo onitoing Pocess Vaiance", Jounal of Quality Technology, Vol. 7, Cowde, S.V. (989). Design of Exonentially Weighted oving Aveages Schemes, Jounal of Quality Technology, Vol., English, J. R., ee S., atin T. W. and Tilmon C. (). "Detecting Changes in Autoegessive Pocesses with and EWA Chats", IIE Tansactions, Vol. 3, Gan, F. F. (99). "An Otimal Design of CUSU Quality Contol Chats", Jounal of Quality Technology, Vol. 3, Gan, F. F. (995). "Joint onitoing of Pocess ean and Vaiance Using Exonentially Weighted oving Aveage Contol Chats", Technometics, Vol. 37, Gan, F. F. (997). "Joint onitoing of Pocess ean and Vaiance", Nonlinea Analysis Theoy, ethods & Alications, Vol. 3(7), Giffith, G. K. (989). Statistical Pocess Contol ethods fo ong and Shot Runs, Ameican Society fo Quality.

17 Hawins, D.. (98). "A CUSU fo a Scale Paamete", Jounal of Quality Technology, 3, Vol. in, W. S. W. and Adams,.. (996). "Combined Contol Chats fo Foecast-ased onitoing Schemes", Jounal of Quality Technology, Vol. 8, u, C. and Reynolds,. R. (999). "EWA Contol Chats fo onitoing the ean of Autocoelated Pocesses", Jounal of Quality Technology, Vol. 3, ucas, J.. (976). "The Design and Use of Cumulative Sum Quality Contol Schemes", Jounal of Quality Technology, Vol. 8,. -. ucas, J.. (98). "Combined Shewhat-CUSU Quality Contol Schemes", Jounal of Quality Technology, Vol. 4, ucas, J.. (985). "Cumulative Sum (CUSU) Contol Schemes", Communications in Statistics - Theoy and ethods, Vol. 4, ucas, J.. and Saccucci,. S. (99). Exonentially Weighted oving Aveage Contol Schemes: Poeties and Enhancements, Technometics, Vol.3,. -9. acgego, J. F. and Hais, T. J. (993). "The Exonentially Weighted oving Vaiance", Jounal of Quality Technology, Vol. 5, astangelo, C.. and ontgomey, D. C. (995). "SPC with Coelated Obsevations fo the Chemical and Pocess Industies", Quality and Reliability Engineeing Intenational, Vol., ontgomey, D. C. (). Intoduction to Statistical Quality Contol, 4. th Edition, Wiley, New Yo. ontgomey, D. C. and Johnson,. A. (976). Foecasting and Time Seies Analysis, cgaw-hill, New Yo. Page, E. S. (954). "Continuous Insection Schemes", iometia, Vol. 4,. -5. Peeia and Requeio (). "Contolo Estatístico de Pequenas Poduções (SPC in Shot Poduction Runs)",. st National Quality Congess, isboa, Potugal. Pyzde, T. (99). Pyzde s Guide to SPC, Vol.,, ASQC Quality Publishing, Inc. Quesenbey, C.P. (997). SPC ethods fo Quality Imovement, John Wiley & Sons, New Yo. Robets, S. W. (959). "Contol Chat Tests ased on Geometic oving Aveages", Technometics, Vol., 39-5.

18 Timme, D. H., Pignatiello, J. J. and ongnece,. T. (-). "Alying an AR() CUSU Contol Chat to Data fom a Chemical Pocess", Quality Engineeing, Vol. 3(), Westen Electic (956). Statistical Quality Contol Handboo, Westen Electic Cooation, Indianaolis. Wheele, D.J. (99). Shot Run SPC, S.P.C. Pess, Knoxville, Tennessee.