Application of the Advanced Quality Improvement Techniques: Case Study

Transcription

1 Applcaton of the Advanced Qualty Improvement Technques: Case Study Vdosav Majstorovc and Tatjana Sbalja Faculty of Mechancal Engneerng, Unversty of Belgrade, Kraljce Marje 6, Belgrade, Serba Faculty of Engneerng Internatonal Management, European Unversty, Cargradska 8, Belgrade, Serba Abstract. Implementaton of the advanced cost-effectve methodologes for product and/or process qualty mprovement s an effectve mean to fulfl or exceeds customer s expectatons. Ths paper presents the analyss of a performance of automatc enamellng process for a non-normal data dstrbuton, conducted wthn the sx sgma project mplemented n a producton system. Drawng on the process analyss results, process optmsaton was performed usng locaton and dsperson modellng. It proved ts effectveness n determnng the sgnfcant effects of process factors on the response mean and varaton, and n obtanng the optmal factors settng of the observed sngle-response process. Keywords: process performance analyss, non-normal dstrbuton, process parameters optmsaton, locaton and dsperson modellng. Introducton The challenge n today s compettve markets s to be on the leadng edge of producng hgh qualty products at mnmum costs. The mplementaton of the advanced qualty mprovement programs, such as sx sgma, could help n mprovng company's compettveness whch s a key ssue n a fast-movng global ndustry. Sx sgma s a dscplned approach for process and/or product qualty mprovement, based on customer qualty requrements. It takes users away from ntuton-based decsons to fact-based decsons. For the exstng system, sx sgma s deployed accordng to DMAIC (Defne-Measure-Analyse-Improve-Control) procedure. Ths paper deals wth a case study performed n a Serban cookware producton system wth the am to reduce waste and cost of poor qualty (COPQ) and mprove the process sgma level, usng sx sgma methodology. In secton, steps of defne and measure stages were presented n bref, followed by detaled presentaton of the process performance analyss for non-normally dstrbuted data. In the mprovement phase, the usage of locaton and dsperson modellng for the process parameters optmsaton was shown. The dscusson regardng the sgnfcance and effectveness of the used technques was also presented. Secton 3 provdes the concludng remarks on the appled technques. J. Frck and B. Laugen (Eds.): APMS, IFIP AICT 384, pp. 8 89,. IFIP Internatonal Federaton for Informaton Processng

2 8 V. Majstorovc and T. Sbalja Sx Sgma Applcaton Ths study llustrates parts of a sx sgma project conducted accordng to DMAIC. In the defne stage, IDEF method was used to map the system, showng detaled presentaton of man processes, sub-processes and actvtes. Pareto analyss was developed to rank the defect types detected n the automatc enamellng process. The major defects were manly related to the product characterstc - pot enamel thckness. Then, Ishkawa dagrams were used to analyse man causes of major defects, showng that the most problematc sub-process s base enamellng []. In order to verfy the measurng system, the detaled measurng system analyss (MSA) was performed n the measure stage (Fgure ). The gage R&R study was conducted to calculate the equpment varaton (repeatablty), operator varablty (reproducblty) and varaton of pot enamel thckness (part-to-part varaton). Snce operators and equpment caused less than % of the total varaton and the gage bas was statstcally nsgnfcant, the measurng system was accepted for the measurement and process analyss [].. Process Performance Analyss for Non-normally Dstrbuted Data Capablty studes are used to predct the overall ablty of a contnuous dstrbuton process to make products wthn the requred specfcatons. Process capablty analyss entals comparng the performance of a process aganst ts specfcatons, thus enablng analyss of prevous and current performance, and benchmarkng. Process capablty and performance ndces were wdely nvestgated as means of summarzng process performance [3], [4]. Several recent studes were dedcated to capablty and performance ndces [5], [6]. The smplest capablty ndex Cp presents the rato of the specfcaton wdth to the natural tolerance spread of a process. To ncorporate the measure of process locaton, Cpk ndex was created [3], [4], consderng how well the process spread s located about the target and the specfcaton lmts. The nterpretaton of the capablty ndces mples the followng assumptons [3]: process stablty; representatve samples; normalty; ndependences of observatons. Capablty ndces show what s achevable rather than what s currently beng acheved. As a response to ths, the process performance ndces Pp and Ppk were developed. Performance ndces are calculated usng the same formulae as for capablty ndces. However, performances ndces do not assume that the process s n-control or s normally dstrbuted and they use all of the data collected (both ponts n- and out-ofcontrol). The process performance ndces make used of the wthn sample standard devaton ncludng both common and specal cause of varaton. Therefore, they provde a more realstc assessment of what s actually beng produced [3]. It s more realstc to use Pp and Ppk than Cp and Cpk as the process varaton cannot be tempered wth by napproprate subgroupng. The essental assumptons for the capablty ndces use are that the process s stable and the output s normally dstrbuted.

3 Applcaton of the Advanced Qualty Improvement Technques 83 Components of Varaton % Contrbuton % Study Var 7 Databy PartNum 5 % Tolerance 6 Sample Range Gage R&R Repeat Reprod R Chart by Operator 3 Xbar Chart by Operator 3 Part-to-Part UCL=4.9 _ R=.6 LCL= _ UCL=6.8 X=59.64 LCL= Average PartNum Data by Operator Operator Operator * PartNum Interacton 3 5 Operator Regresson 95% CI Data 5 3 PartNum Gage Lnearty Predctor Coef SE Coef P C onstant Slope Avg Bas S.8755 R-Sq 76.% Lnearty.6387 % Lnearty.7 Bas 5 Gage Bas Reference Bas %Bas P A v erage *. 5.3 *. 5.3 * * * Percent of Process Varaton -5 3 Reference Value 4 5 Percent 5 Lnearty Bas Fg.. Detals of MSA: gage R&R (up) and lnearty and bas study (down) When the dstrbuton s non-normal, capablty ndces calculated usng conventonal methods could often lead to erroneous conclusons. If the capablty ndces based on the normal assumpton are used to deal wth non-normal observatons, the values of the capablty ndces may be ncorrect and qute lkely msrepresent the actual process and product qualty [4]. For non-normal dstrbutons, by replacng the unknown 6σ dstance by Up - Lp calculated based on the avalable sample data usng the estmates of the mean, standard devaton, skewness and kurtoss, a natural tolerance s [4], [5]: Tolerance = Up - Lp = X - X () natural

4 84 V. Majstorovc and T. Sbalja where: Up and Lp estmate the and the.35 percentle, respectvely, to mtate the normal dstrbuton property that the tal probablty that the process s outsde ±3σ lmts from the average equals.7%; X.35 and X are values that meet the condtons: P(X<X.35 )=.35, and P(X<X )=.99865, respectvely. Values X and X.35 are the z-values of the non-normal cumulatve dstrbuton curve at the % pont and the.35 % pont, respectvely. The dstance between the th and.35 th percentles s equvalent to 6σ spread n the normal case. The process medan s presented by the 5 th percentle for the non-normal dstrbuton, whch s equvalent to the average value for normal dstrbuton. The relatons above were concluded from Clements method of determnng percentles based on Pearson famly of dstrbuton. Clements developed a method for capablty ndces calculaton for non-normal dstrbutons, utlsng Pearson curves to provde accurate estmates of X.3, X.5 and X.99865, and based on the skewness and kurtoss assessment [4]. Snce the process performances calculaton does not requre the assumpton that the data are normally dstrbuted, t makes sense to evaluate process performance ndces n dscussng the actual process for non-normal data. Based on the relaton (), the process performance ndces for non-normal dstrbuton could be formulated as: USL LSL Pp =, X - X USL X.5 X.5 LSL Ppk = mn ; () X X.5 X.5 - X.35 Process Data LSL 8 Target 95 USL Sample Mean 3,75 Sample N 95 Shape 6,38 Scale 5,84 Observed Performance PPM < LSL, PPM > USL, PPM Total, LSL Target USL O verall C apablty Pp,6 PPL, PPU,66 Ppk, Exp. Overall Performance PPM < LSL 683,3 PPM > USL, PPM Total 683, Fg.. Performance of the base enamellng process for a Webull dstrbuton In the observed sx sgma project, as a part of Statstcal Process Control (SPC) mplementaton, the analyss of the base enamellng process was performed usng X, R control chart and process capablty and performance analyss. Specfcaton lmts for base enamel thckness are: LSL USL=8 μm; the specfed target value s 95 μm.

5 Applcaton of the Advanced Qualty Improvement Technques 85 After concludng that the process s statstcally stable, process probablty plot showed that the process data are not normally dstrbuted. Several probablty plots for dfferent non-normal dstrbutons were tested, and the Webull dstrbuton s found the best one to ft the actual process data. The Anderson-Darlng goodness-of-ft test and p-value test were used to evaluate the hypothess that the Webull dstrbuton provdes the best ft. Capablty plot for Webull dstrbuton showed that the actual overall process tolerance nterval s contaned wthn the specfcaton nterval. Fgure presents the base enamellng process performance for a Webull dstrbuton. The process capablty estmaton was performed usng the overall process performance ndces calculated usng relaton (). Pp value of.6 shows that the process s capable of producng at least % of conformng parts. Snce Pp s greater than Ppk and PPU s greater that PPL, the process medan s off the target and closer to USL. Ths clearly ndcates the locaton problem. The non-conformance rate s estmated as 683 parts per mllon.. Process Parameters Optmsaton Usng Locaton and Dsperson Modellng If the process s not capable of producng vrtually all conformng products, t s necessary to mprove process performance usng advanced expermentaton methods, such as Taguch robust parameter desgn. Taguch s orthogonal expermentaton s frequently adopted to reduce the trals number but stll obtan reasonably rch nformaton wth certan statstcal level of confdence. Robust parameter desgn was successfully used n optmsng many sngle-response processes, optmsng both the mean and the varance of a response, makng a process mmune to nose sources, and ultmately mprovng process and/or product qualty. In a modern ndustry, demands for short lfe cycles and hghqualty products requre effcent and objectve use of expermentaton. Wth the lmted amount of data provded n an unreplcated experment based on orthogonal array, t s very demandng to study both locaton and dsperson effects. The dentfcaton of the control factor effects on locaton (mean) and dsperson (varaton) of the observed qualty characterstc (response) has been proven effectve n many sngle-response process optmsatons [7], [8], [9]. The locaton and dsperson modellng approach gves models for measures of locaton and dsperson separately, n term of control factors and nteractons man effects on a response. At each control factors settng, the sample mean y and sample varance σ (where n s number of replcates at for the th control factors settng), are used to present the locaton and dsperson [7]: γ = y, σ ( ) j y y j n = (3) n j The half-normal probablty plot s a graphcal tool that uses ordered estmated effects to help assess whch factors are mportant. A half-normal dstrbuton s the dstrbuton of the Y wth Y havng a normal dstrbuton. Quanttatvely, the estmated effect of a gven man effect or nteracton and ts rank relatve to other man effects and nteractons s gven va least squares estmaton. Unmportant factors are those that have near-zero effects and mportant factors are those whose effects are consderably removed from zero. Hence, unmportant effects tend to have a normal dstrbuton centred near zero whle mportant effects tend to have a normal dstrbuton centred at ther respectve true large (but unknown) effect values [9]. j

6 86 V. Majstorovc and T. Sbalja From the analyss presented n secton. t was concluded that the process needs optmsaton n order to solve the locaton problem (acheve the target base enamellng thckness) and mprove process performance. An experment was performed to dentfy the optmal settng of crtcal-to-qualty (CTQ) control factors. The parameters adopted as control factors and ther values used n the experment (Table ) are: enamel parameters: SW, DW, and SW DW nteracton; process parameters: PS, AS, and PS AS nteracton. In order to accommodate four control factors and two nteractons studed at two levels, orthogonal array L6 was used to desgn the expermental plan []. Table. Control factors and levels used n the experment Control factor Symbol Unt Level '-' Level '+' Specfc weght SW gram cm -3 8 Depost weght DW gram cm -3,68,7 Pourng speed PS turns mn - 3 Automat speed AS parts mn Half-normal plots were developed to show the sgnfcance of the effects of control factors and ther nteractons on the response (base enamellng thckness) locaton and dsperson. Half-normal plot for the response locaton (MEAN) s shown at Fgure 3 up. From the locaton plot t s vsble that effects of factors SW, DW, PS and nteracton AS SW DW are sgnfcant. Then, the regresson analyss for the response locaton (MEAN) was conducted, showng regresson equaton as follows: MEAN = SW DW + 3. SW DW AS PS (4) Table shows statstcal parameters for the regresson equtaton (4). The above sgnfcant control factors and nteracton for the response locaton are used as predctors. Each predctor n a regresson equaton has a coeffcent assocated wth t. In multple regressons the estmated coeffcent (Coef.) ndcates the change n the mean response per unt ncrease n the respondng predctor when all other predctors are held constant. If the p-value of a coeffcent s less than the α-level (α=.5), there s evdence of a sgnfcant relatonshp between the predctor and the response. Value T s used for comparson wth the t-dstrbuton to determne f a predctor s sgnfcant. Fgure 3 down shows the half-normal plot for the response dsperson, presented over Ln Sgma. The reason to use the natural logarthm s that t maps postve values to real (both postve and negatve) values, and by takng ts nverse transformaton, any predcted value on the ln scale wll be transformed back to a postve value on the orgnal scale. Also, ln transformaton converts a possble multplcatve relatonshp nto an addtve relatonshp, whch s easer to model statstcally [7]. The dsperson plot shows sgnfcant effects of PS, PS AS, DW and PS DW for the response dsperson. Statstcal parameters for the dsperson regresson equtaton are gven n Table. The obtaned regresson equaton for the response dsperson (Ln Sgma ) s: LnSgma = PS +. PS AS +.9 DW +. 6 DW PS (5)

7 Applcaton of the Advanced Qualty Improvement Technques 87 SW. DW.5 AS*SW*DW PS SW*DW. AS AS*DW PS*AS*SW*DW PS*SW*DW AS*SW.5 PS*AS PS*AS*DW PS*AS*SW PS*SW PS*DW PS 4. PS*AS.5 DW PS*DW AS*DW..5.. PS*SW SW PS*AS*SW*DW PS*AS*DW SW*DW PS*SW*DW AS*SW*DW PS*AS*SW AS*SW AS Fg. 3. Half-normal plot of locaton (up) and dsperson (down) effects Snce the objectve of the experment s to acheve the nomnal (target) response mean value, and followng the two-step procedure for Nomnal-the-Best (NTB) problems [7], the frst step s to select the levels of dsperson factors to mnmse dsperson. From the dsperson effects relaton (5), n order to mnmse dsperson the followng levels of dsperson factors are selected: PS level '-', AS level '+'. The factor SW could be used to brng the mean on the target (value 95 μm), dependng on DW level. Ths s presented n the equtaton (6), obtaned from the locaton effects relaton (4): 95 = SW DW + 3. SW DW ( + ) +,79 ( ) (6)

8 88 V. Majstorovc and T. Sbalja There are two possble solutons of the equtaton (6): (a.) f DW s set to level '-' then calculated SW s 6.; (b.) f DW s set to level '+' calculated SW value s.5. Snce due to machne lmtaton t s mpossble n practce to set the SW value to 6., the second soluton s adopted resultng n the fnal optmal control factors settng: DW=.7; SW=; PS=; AS=9. Table. Statstcal parameters of regresson equtaton for locaton and dsperson modellng Locaton modellng Dsperson modellng Predctor Coef. T P Predctor Coef. T P Constant Constant SW PS DW PS AS SW DW AS DW PS DW PS Dscusson Process analyss performed under the assumpton of normally dstrbuted data provded hghly msleadng results, showng that process performance ndces are hgher than capablty ndces, whch s practcally mpossble. Ths hghlghts the mportance of the accurate process performance calculaton, provdng correct data for the customer and for the process mprovement. Based on the conclusons drawn from the process analyss for a non-normal dstrbuton, the experment was performed to optmse the process wth respect to the target value for the product s characterstc mean (locaton) and to reduce varaton (dsperson). The expermental analyss was performed usng ANOVA and usng locaton and dsperson modellng. Although both methods dsplayed the same optmal factors settng, the later showed sgnfcant nteracton effects on mean (AS SW DW) and varaton (PS DW), that ANOVA dd not detect []. Verfcaton run was performed usng optmsed factors settng, confrmng the expermental results. The obtaned results present sgnfcant mprovement n comparson to the prevous performance. Accordng to Taguch's qualty loss functon, loss caused by prevous performance was Lp(Y) = K 7.6 unts [], and loss encountered after optmsaton s Lo(Y) = K.99 unts. The acheved mprovements are montored n a practce and documented to ensure the sustanablty. Sgnfcant reducton of a waste, COPQ and non-added-value actvtes rework and nspecton, and mprovement of process performance are expected to be sustaned. 3 Concludng Remarks Important ssues regardng process analyss and mprovement have been hghlghted n ths study. The sgnfcance of the accurate estmaton of process performance ndces for non-normal dstrbuton was shown. The use of the locaton and dsperson modellng clarfed a total contrbuton to the process varaton, and t was shown as a successful method to optmse the observed sngle-response process.

9 Applcaton of the Advanced Qualty Improvement Technques 89 However, t would be dffcult to apply the presented method for the multresponse process optmsaton. Therefore, the authors developed the method conssted of two stages. In the frst stage, a statstcal factor effects approach was developed, based on Taguch's qualty loss functon, prncpal component analyss and grey relatonal analyss, to uncorrelated and synthess responses nto a sngle measure. Snce ths approach could not provde the overall global optmum, n the second stage the ntellgent approach was developed usng neural networks (to model the process behavour) and a genetc algorthm (GA) (to perform search n a contnual space), to ensure that the actual global optmum s found []. The method was further mproved usng smulated annealng (SA) as the optmsaton tool, nstead of GA []. Implementaton of sx sgma presented frst steps n ntroducng the advanced qualty mprovement programs n Serban ndustry. Whle sx sgma s wdespread adopted as a prmary qualty mprovement program among a varety of ndustres, authors stressed on the mportance of a busness culture changes and a theoretcal underpnnng, n order to brdge the gap between the theory and practce of sx sgma methodology. References. Majstorovc, V., Sbalja, T.: An Applcaton of DMAIC Approach to Process Qualty Improvement Case Study. In: Proceedngs of IFAC Workshop on Manufacturng, Modellng, Management and Control - MIM 7, pp. 8 (7). Cagnazzo, L., Sbalja, T., Majstorovc, V.: The Measurement System Analyss as a Performance Improvement Catalyst: a Case Study. In: Tatcch, P. (ed.) Busness Performance Measurement and Management, New Contents, Themes and Challenges, pp Sprnger, Hedelberg () 3. Keats, J.B., Montgomery, D.C.: Statstcal Applcatons n Process Control. Marcel Dekker, Inc., New York (996) 4. Pearn, W.L., Kotz, S.: Encyclopaeda and Handbook of Process Capablty Indces. World Scentfc Publshng Co. Ltd., Sngapore (6) 5. Rezae, K., Ostad, B., Taghzadeh, M.R.: Applcatons of Process Capablty and Process Performance Indces. Journal of Appled Scences 6, 86 9 (6) 6. Chen, J.-P., Dng, C.G.: A new process capablty ndex for non-normal dstrbutons. Int. J. Qual. Relab. Manag. 8, () 7. Wu, C.F.J., Hamada, M.: Experments Plannng, Analyss and Parameter Desgn Optmsaton. John Wlley & Sons Inc., New York () 8. Wang, P.C., Ln, D.F.: Dsperson effects n sgnal-response data from fractonal factoral experments. Computatonal Statstcs & Data Analyss 38, 95 () 9. McGrath, R.N., Ln, D.K.J.: Analyzng locaton and dsperson n unreplcated fractonal factoral experments. Statstcs & Probablty Letters 65, (3). Sbalja, T., Majstorovc, V., Rosu, S.M.: Locaton and dsperson effects n sngle-response system data from Taguch orthogonal expermentaton. In: Proceedngs n Manufacturng Systems, vol. 4, pp Romanan Academy Publshng House, Bucharest (9). Sbalja, T., Majstorovc, V.: An ntegrated approach to optmse parameter desgn of mult-response processes based on Taguch method and artfcal ntellgence. J. Intell. Manuf. (), do:.7/s y. Sbalja, T., Majstorovc, V.: An ntegrated smulated annealng-based method for robust multresponse process optmsaton. Int. J. Adv. Manuf. Technol. 59(9), 7 44 ()