Statistical Process Control in Service Industry An Application with Real Data in a Commercial Company

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1 Statstcal Process Control n Servce Industry An Applcaton wth Real Data n a Commercal Company A. Scordak and S. Psaraks Abstract- The man purpose of ths artcle s to present the advances of Statstcal Process Control technques n nonmanufacturng processes. Specfcally, n ths artcle we present two applcatons of control chartng technques n a commercal company. The frst s an applcaton of control chartng technques n the Sales Department and the second s an applcaton of control charts n the Logstc Departments. Index Terms- Qualty Control; Process Control; Servce Industry; Multvarate Control Charts; Process Flow; Qualty Control Implementaton; Servce Qualty; Statstcal Process Control; Statstcal Qualty Control; Servces. I. INTRODUCTION The prncpal applcaton doman for statstcal process control (SPC) charts has been for process control and mprovement n manufacturng busnesses for about ffty years. The most common process control technque has been control chartng. A control chart s a useful statstcal tool that ads practtoners n statstcally controllng and montorng one or more varables, when the qualty of the product or the qualty of the process s characterzed by certan values of ths or these varables. By the term controllng, we mean the ablty of the control chart at any tme to determne f the process or the product characterstc s statstcally n control. The term statstcally n control process reflects to a process that operates wth only chance causes of varaton. A process that s operatng n the presence of assgnable causes s sad to be statstcally out-of-control. In General, a control chart s very easy to be mplemented n any type of process. Thus, control charts are extensvely used n manufacturng area nowadays, preservng the qualty of the process or the fnal product. The controllng and montorng s done over ether the mean level or the varance of the process or qualty characterstc. Montgomery [4] provdes an excellent dscusson about statstcal process control procedures n the manufacturng ndustry. However, the number of applcatons reported n domans outsde of conventonal producton systems has been Broscor S.A., Department of Logstcs, Athens, Greece Athens Unversty of Economc and Busness, Department of Statstcs, Athens, Greece ncreasng n recent years. Implementng SPC chart approaches n non-standard applcatons gves rse to many potental complcatons and poses a number of challenges. Woodall and Montgomery [9] note that there s a contnung need for publcatons of case studes showng the benefts of SQC generally. Tll the year 4, more than 8 artcles, have been dentfed n the lterature that deal wth non-standard applcatons of SPC charts. Broadly four applcaton domans are manly dentfed: () engneerng, ndustral and envronmental applcatons; () healthcare applcatons; (3) general servce sector applcaton; (4) statstcal applcatons. Four prncpal obectves have been dentfed for the reported studes: () Process montorng. Ths s an extenson of the conventonal applcatons of control charts to a much wder range of processes. As wth conventonal applcatons, the obectves are to montor and control a process n order to mantan process stablty and n many cases to enable process mprovement. For ths group of applcatons t s worth dstngushng between those applcatons for whch conventonal Shewhart chartng technques are deemed approprate and those applcatons that requre other technques. () Plannng. SPC charts are used n a number applcaton domans to derve effectve plans or schedules, partcularly for mantenance schedulng. Ths may be a type of applcaton for SPC charts wth potental for wder use. (3) Evaluatng customer satsfacton. SPC charts are used to evaluate customer satsfacton n a range of applcaton domans to detect hgh levels of satsfacton and dssatsfacton. Ths may also be a type of applcaton for SPC charts wth potental for wder use. (4) Forecastng. SPC charts are used to generate or optmse a forecastng model. Ths may be consdered a statstcal or techncal applcaton of SPC charts wth some potental for wder use specfcally n forecastng applcatons. In ths artcle we present the advances of Statstcal Process Control technques n non-manufacturng processes. Specfcally, n Secton, we gve a bref revew of the lterature n the area of non-manufacturng applcatons of statstcal process control. Furthermore, n Secton 3 we brefly dscuss the man characterstcs of Shewhart type control charts. Fnally, n Secton 4, we dscuss an applcaton of control chartng technques n the Sales Department. Fnally, n Secton 5 we pont out some concludng remarks and topcs for further research.

2 II. REVIEW A number of researchers have proposed frameworks, mplementaton steps or gven caveats for practtoners, who want to mplement control charts n varous nonmanufacturng domans (Atenza et al. []; Beamon and Ware []; Benneyan [3,4] Does et al. [6]; Duffuaa and Ben- Daya [8]; Fnson et al. [9]; Humble []; Lews []; Roes and Dorr [5]; Sellck [6]; Wood [8]). Beamon and Ware [] propose a framework whch provdes a methodology to mplement a qualty system for a supply chan process. Wood [8] proposes SPC chart gudelnes n servce processes. Fnson et al. [9] and Sellck [6] dscuss fundamental control chart theory n the context of mplementng SPC charts n healthcare applcatons. Does et al. [7] also notes the need for commtment of top management before the ntaton of an SPC proect. Sulek [7] argued that the under-utlsaton of statstcal qualty control technques n the servce ndustry results from an ncomplete conceptualzaton of servce qualty. She ntroduced a systems framework for servce process qualty whch s used to dffuse popular arguments aganst the use of statstcal qualty control n servces. MacCarthy and Wasusr [3] gave an excellent revew n the lterature of non-manufacturng SPC uses. In ths paper, we ntroduce some ndces for measurng the ablty of the sale s process of a Hellenc commercal company n order to apply statstcal process control and montorng. Statstcal process control technques are wdely used n ndustry. The most common process control technque s control chartng. III. SHEWHART TYPE CONTROL CHARTS A Shewhart type control chart s a graphcal dsplay of a process or a product qualty characterstc that has been measured or computed from a sample versus the sample number or tme. The basc characterstcs of a unvarate Shewhart process control chart are the «Center Lne» (C.L), the «Upper Control Lmt» (U.C.L), and the «Lower Control Lmt» (L.C.L). The ordnary rule appled to a Shewhart type control chart for declarng a possble out-of-control condton n a manufacturng process s the occurrence of a pont outsde the control lmts. For example, n Fgures and, control charts for controllng the mean and the varance of qualty characterstcs are gven. In addton, many senstzng run rules have been suggested for the Shewhart control charts n order to make them more senstve n the detecton of drfts n the mean of the process. There are two dstnct phases of control chartng, Phase I and Phase II. In Phase I, charts are used for retrospectvely testng whether the process was n control when the frst subgroups were beng drawn. In ths phase, the charts are used as ads to the practtoner, n brngng a process nto a state of statstcal n-control. Once ths s accomplshed, the control chart s used to defne what s meant by statstcal n-control. In Phase II, control charts are used for testng whether the process remans n control when future subgroups are drawn Chart for Length UCL = 43,85 CTR = 99,98 LCL = 56, Fgure : A classc Shewhart Type control chart MR() MR() Chart for Length UCL = 53,9 CTR = 6,49 LCL =, Fgure : A classc Shewhart Type MR control chart In Phase I, Shewhart control charts are very effectve, snce they are easy to construct and the nterpretaton s clear. Specfcally, the meanng of a pattern appearng n a Shewhart type control chart s straghtforward and has a physcal meanng. These run rules were frst proposed by the Western Electrc Company []. IV. METHODOLOGY FOR APPLYING CONTROL CHARTS TO SALES DEPARTMENT In ths Secton we present the basc deas of applyng Shewhart type control charts n sales data. The company that concerns ths study s a commercal enterprse n the area of furnshng. The department of sales conssts of k salesmen. The data that we have n our hands concern the weekly sales of each one of the k salesmen, from July, 974 tll February, 5 5 (n=5 fve days a week measurements, and m =3 weeks n total). Furthermore, we defne the weekly sales of each salesman by S for =,,.., 3 and =,,..,k. The sum of sales of k salesmen wll be symbolzed wth S S for =,,.., 3. T s sum of the k random varables. The rato of the sales of each salesman weekly as for the total sales of the week s defned as R for =,,.., 3 and =,,..,k. T

3 Thus, n order to check the stablty and the attrbuton of each salesman we may apply k ndependent Shewhart type control charts for ndvdual observatons. Furthermore, we wll suppose that the sales of the k salesmen are ndependent among them. Actually, ths cannot be vald, snce the sales of each one of salesmen s nfluenced by the state of sector s market, whch s reflected n the total sales of the company. Another assumpton that we make s that the weekly sales of each salesman are tme ndependent. Such a hypothess also may not be vald because of the fact that the sales are nfluenced from seasonalty n the partcular market. Fnally, we suppose that the sales follow the normal dstrbuton. Ths hypothess may be verfed. Applyng Shewhart type control charts for ndvdual observatons S n each one of the k salesmen, gnorng the cross-correlaton and also gnorng the autocorrelaton of measurements, we may drve the wrong concluson that the sales actvty s out-of-control. In Fgure 3, the control chart for ndvdual observatons for controllng the mean weekly sales as well as n Fgure 4, the approprate control chart for montorng the varance of sales actvty for the salesman D are gven. In order to take nto account the cross-correlaton among varables, a multvarate control chart may be appled. Ths control chart s known as the T Shewhart type control chart (Hotellng [], Bersms [5]). ( ) Chart for D UCL = 9339, CTR = 4533,4 LCL = -7,34 Fgure 3: The control chart for controllng the weekly (mean) sales Salesman D. ( ) 8 MR() 6 4 MR() Chart for D UCL = 596, CTR = 86,9 LCL =, Fgure 4: The control chart for controllng the dsperson of the weekly (varance) sales Salesman D. Pr(accept),8,6,4, OC Curve for ( ) Process mean Fgure 5: The Operatng Characterstc Curve of the control chart T-Squared Multvarate Control Chart 3 UCL = 5,54 Fgure 6: The control chart for controllng the weekly (mean) sales of all the salesmen. As t appears n Fgure 6, the sales of k salesmen actually are under a stable state, meanng that the sale process s statstcally n-control. Examng more carefully the T control chart we may observe a non-random repeated pattern. Ths means that the T values for =,,.., 3 may be nsde the control lmts but they are far away from the lne (base of graph). Ths fact s owed n the autocorrelaton. As we may easly conclude by observng Fgures 7 and 8, there s a statstcally sgnfcant autocorrelaton among the values of the T. Furthermore, when we face such a problem we have two choces. The frst choce, s to model our observatons makng use of some sutable tme seres model. However, the problem of ndependent control of each one of salesmen wll stll reman. For ths reason, we selected the second S alternatve, n order to control the quantty R =. T S The use of ths quantty allows us almost the ndependent control of each salesman, snce n ths way we remove a sgnfcant part of the autocorrelaton among observatons. Ths R ndcator s the rato of two related normal random varables and ts dstrbuton s known. Usng the above defned rato and by observng Fgures 9 and, we may see (that the prevous extracted concluson that the sales process of the salesman D s out-of-control) s false.

4 Autocorrelatons Estmated Autocorrelatons for SUM,6, -, -, lag Fgure 7: A classc Shewhart Type MR control chart Partal Autocorrelatons Estmated Partal Autocorrelatons for SUM,6, -, -, lag Fgure 8: A classc Shewhart Type MR control chart V. COMMENTS AND TOPICS FOR FURTHER RESEARCH The am of ths artcle s to present the potental uses of control chartng n non-ndustral processes. The use of the statstcal qualty control procedures n commercal companes or/and generally n non-ndustral processes may be a valuable tool n the machnery of the managers n evaluatng employees, departments, and servces.,7,5,3, -, Chart for P_C UCL =,64 CTR =,8 LCL = -,9 Fgure 9: The control chart for controllng the weekly (mean) sales Salesman D based on the R C. MR(),5,4,3,, MR() Chart for P_C UCL =,45 CTR =,4 LCL =, Fgure : The control chart for controllng the dsperson of the weekly (varance) sales Salesman D based on the R C. ACKNOWLEDGMENT A. Scordak thanks the Broscor S.A. for permttng to her usng the data fles of the company. REFERENCES []. Atenza, O.O., Ang, B.W. and Tang, L.C. (997), ``Statstcal process control and forecastng, Internatonal Journal of Qualty Scence, Vol. No., pp []. Beamon, B.M. and Ware, T.M. (998), ``A process qualty model for the analyss, mprovement and control of supply chan systems, Internatonal Journal of Physcal Dstrbuton & Logstcs Management, Vol. 8 No. 9/, pp [3]. Benneyan, J.C. (998a), ``Statstcal qualty control methods n nfecton control and hosptal epdemology, part I: ntroducton and basc theory, Infecton Control and Hosptal Epdemology, Vol. 9 No. 3, pp [4]. Benneyan, J.C. (998b), ``Statstcal qualty control methods n nfecton control and hosptal epdemology, part II: chart use, statstcal propertes, and research ssues, Infecton Control and Hosptal Epdemology, Vol. 9 No. 4, pp [5]. Bersms, S. Multvarate Statstcal Process Control, M.Sc. Thess, Department of Statstcs, Athens Unversty of Economcs and Busness,, ISBN [6]. Does, R.J.M.M., Schppers, W.A.J. and Trp, A. (997), ``A framework for mplementaton of statstcal process control, Internatonal Journal of Qualty Scence, Vol. No. 3, pp [7]. Does, R.J.M.M., Roes, K.C.B. and Trp, A. (999), Statstcal Process Control n Industry, Kluwer Academc Publshers, Dordrecht. [8]. Duffuaa, S.O. and Ben-Daya, M. (995), ``Improvng mantenance qualty usng SPC tools, Journal of Qualty nmantenance Engneerng, Vol. No., pp [9]. Fnson, L.J., Fnson, K.S. and Blersbach, C.M. (993), ``The use of control charts to mprove healthcare

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