Hotelling’s control chart, Adjusted Average Time to Signal (AATS), Variable Parameters (VP), Economic Statistical Design (ESD), Wald’s identity, Multi-objective Genetic Algorithm (MOGA).
Abstract :
[en] Recent studies have shown that applying the control chart by using a variable parameters (VP) scheme yields more rapid detection of assignable causes than the classical method of taking fixed sample sizes at fixed intervals of time. In this paper, the problem of economical statistical design of the VP T2 control chart is considered as a double-objective minimization problem with the statistical objective adjusted average time to signal and the economic objective expected cost per hour. Then we strive to find the Pareto-optimal designs in which the two objectives are met simultaneously by using a multi-objective Genetic Algorithm or GA. Through an illustrative example, we show that relatively large benefits accrue to the VP method relative to the classical policy; further another advantage of our approach is to provide a list of alternative solutions that can be explored graphically. This then ensures flexibility and adaptability, an important attribute of contemporary control chart design.
Disciplines :
Quantitative methods in economics & management
Author, co-author :
Faraz, Alireza ; Université de Liège - ULiège > HEC-Ecole de gestion : UER > Statistique appliquée à la gestion et à l'économie
Heuchenne, Cédric ; Université de Liège - ULiège > HEC-Ecole de gestion : UER > Statistique appliquée à la gestion et à l'économie
Saniga, Erwin; Department of Business Administration, University of Delaware, Newark, Delaware 19716, USA
Costa, Antonio F.B.; Department of Production, FEG-UNESP, Guaratingueta& , SP 12500-000, Brazil
Language :
English
Title :
Double Objective Economic Statistical Design of the VPT2 Control Chart: Wald’s identity approach
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Bibliography
Hotelling H. Multivariate quality control - illustrated by the air testing of sample bombsights. In: Eisenhart C, Hastay MW, Wallis WA, editors. Techniques of statistical analysis. New York: McGraw-Hill; 1947. p. 111-184.
Fuchs C, Kenett RS. Multivariate quality control, theory and applications. New York, NY: Marcel Dekker; 1998.
Mason RL, Young JC. Multivariate statistical process control with industrial applications. Philadelphia, PA: ASASIAM; 2002.
Lowry CA, Montgomery DC. A review of multivariate control charts. IIE Trans. 1995;27:800-810. doi: 10.1080/07408179508936797
Woodall WH, Spitzner DJ, Montgomery DC, Gupta S. Using control charts to monitor process and product quality profiles. J Qual Technol. 2004;36:309-320.
Costa AFB. X-bar charts with variable sampling size. J Qual Technol. 1994;26:155-163.
Aparisi F. Hotelling's T2 control chart with adaptive sample sizes. Int J Prod Res. 1996;34:2853-2862. doi: 10.1080/00207549608905062
Zimmer LS, Montgomery DC, Runger GC. Evaluation of a three-state adaptive sample size control chart. Int J Prod Res. 1998;36:733-743. doi: 10.1080/002075498193660
Faraz A, Moghadam MB. Hotelling's T2 control chart with two-state adaptive sample size, quality & quantity. Int J Methodol. 2009;43:903-913. doi: 10.1007/s11135-008-9167-x.
Runger GC, Pignatiello JJ. Adaptive sampling for process controls. J Qual Technol. 1991;23:135-155.
Runger GC, Montgomery DC. Adaptive sampling enhancements for Shewhart control charts. IIE Trans. 1993;25:41-51. doi: 10.1080/07408179308964289
Aparisi F, Haro CL. Hotelling's T2 control chart with variable sampling intervals. Int J Prod Res. 2001;39:3127-3140. doi: 10.1080/00207540110054597
Faraz A, Chalaki K, Moghadam MB. On the properties of the Hotelling's T2 control chart with VSI scheme, quality & quantity. Int J Methodol. 2011;45:579-586. doi: 10.1007/s11135-010-9314-z.
Reynolds MRJr. Variable sampling interval control charts with sampling at fixed times. IIE Trans. 1996;28:497-510. doi: 10.1080/07408179608966297
Prabhu SS, Montgomery DC, Runger GC. A combined adaptive sample size and sampling interval X-bar control scheme. J Qual Technol. 1994;26:164-176.
Costa AFB. X-bar charts with variable sample size and sampling intervals. J Qual Technol. 1997;29:197-204.
Park C, Reynolds MRJr. Economic design of a variable sampling rate X-bar chart. J Qual Technol. 1999;31:427-443.
Zimmer LS, Montgomery DC, Runger GC. Guidelines for the application of adaptive control charting schemes. Int J Prod Res. 2000;38:1977-1992. doi: 10.1080/002075400188447
Reynolds MRJr., Arnold JC. EWMA control charts with variable sample sizes and variable sampling intervals. IIE Trans. 2001;33:511-530.
De Magalhaes MS, Costa AFB, Epprecht EK. Constrained optimization model for the design of an adaptive X-bar chart. Int J Prod Res. 2002;40:3199-3218. doi: 10.1080/00207540210136504
Aparisi F, Haro CL. A comparison of T2 charts with variable sampling scheme as opposed to MEWMA. Int J Prod Res. 2003;41:2169-2182. doi: 10.1080/0020754031000138655
Faraz A, Parsian A. Hotelling's T2 control chart with double warning lines. Statistical paper. 2006:43.
Tagaras G. A survey of recent developments in the design of adaptive control charts. J Qual Technol. 1998;30:212-231.
Costa AFB. Xbar charts with variable parameters. J Qual Technol. 1999;31:408-416.
Chen YK. Adaptive sampling enhancement of Hotelling's T2 control charts. Eur J Oper Res. 2007;178:841-857. doi: 10.1016/j.ejor.2006.03.001
Duncan AJ. The economic design of X-bar charts used to maintain current control of a process. J Amer Statist Assoc. 1956;51:228-242.
Woodall WH. Weaknesses of the economical design of control charts. Technometrics. 1986;28:408-409. doi: 10.2307/1269000
Saniga EM. Economic statistical control chart designs with an application to and R charts. Technometrics. 1989;31:313-320.
Montgomery DC, Woodall WH. A discussion on statistically based process monitoring and control. J Qual Technol. 1997;29:121-162.
Chen YK. Economic design of variable sampling interval T2 control charts-a hybrid Markov chain approach with genetic algorithms. Expert Syst Appl. 2007;33:683-689. doi: 10.1016/j.eswa.2006.06.007
Chen YK. Economic design of variable T2 control chart with the VSSI sampling scheme. Qual Quant. 2009;14:109-122. doi: 10.1007/s11135-007-9101-7
Faraz A, Kazemzade RB, Saniga E. Economic and economical statistical design of Hotelling's T2 control chart with two-state adaptive sample size. J Stat Comput Simul. 2010;80(12):1299-1316. doi: 10.1080/00949650903062574
Faraz A, Saniga E. Economic and economic statistical design of Hotelling's T2 control chart with double warning lines. Qual Reliab Eng Int. 2011;27:125-139. doi: 10.1002/qre.1095
Saniga E, McWilliams T, Davis D, Lucas J. Economic control chart policies for monitoring variables. Int J Prod Qual Manag. 2006;1:116-138.
De Magalhaes MS, Epprecht EK, Costa AFB. Economic design of a VP X-bar control chart. Int J Prod Econ. 2001;74:191-200. doi: 10.1016/S0925-5273(01)00126-8
Celano G, Costa AFB, De Magalhaes MS, Fichera S. A stochastic shift model for economically designed charts constrained by the process stage configuration. Int J Prod Econ. 2011;132(2):315-325. doi: 10.1016/j.ijpe.2011.05.003
Celano G, Fichera S. Multiobjective economic design of a control chart. Comput Ind Eng. 1999;37:129-132. doi: 10.1016/S0360-8352(99)00038-8
Faraz A, Saniga E. Multiobjective genetic algorithm approach to the economic statistical design of control charts with an application to Xbar and S2 charts. Qual Reliab Eng Int. 2013;29:407-415. doi: 10.1002/qre.1390
Wald A. On cumulative sums of random variables. Ann Math Stat. 1944;15(3):283-296. doi: 10.1214/aoms/1177731235
Lorenzen TJ, Vance LC. The economic design of control charts: a unified approach. Technometrics. 1986;28:3-11. doi: 10.1080/00401706.1986.10488092
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