[en] T2 control charts are used to monitor a process when more than one quality variable associated with the process is being observed. Recent studies have shown that using variable sampling size (VSS) schemes results in charts with more statistical power for detecting small to moderate shifts in the process mean vector. This paper presents an economic-statistical design of T2 control charts with variable sample size and control limits (VSSC). We build a cost model of a VSSC T2 control chart for the purpose of economic-statistical design using the model of Costa and Rahim (J. Appl. Stat. 28:875–885, 2001). This cost model constructed involves the cost of false alarms, the cost of finding and eliminating an assignable cause, the cost associated with production in an out-of-control state, and the cost of sampling and testing. We optimize this model using a genetic algorithm approach. Furthermore, VSSC and VSS T2 charts are compared with respect to the expected cost per unit time.
Disciplines :
Quantitative methods in economics & management
Author, co-author :
Seif, Asghar; Islamic Azad University, Hamedan Branch > Department of Mathematics
Moghadam, M.B.; Allameh Tabatabaee University, Tehran, Iran > Department of Statistics
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
Language :
English
Title :
Statistical Merits and Economic Evaluation of T2 Control Charts with the VSSC Scheme
Costa A. F. B., Rahim M. A.: Economic design of X̄ charts with variable parameters: the Markov Chain approach. J. Appl. Stat. 28, 875-885 (2001).
Serel, D. A.: Economic design of EWMA control charts based on loss function. Math. Comput. Model. (2008). doi: 10. 1016/j. mcm. 2008. 06. 012.
Burr I. W.: Control charts for measurements with varying sample sizes. J. Qual. Technol. 1, 163-167 (1969).
Daudin J. J.: Double sampling X̄ charts. J. Qual. Technol. 24, 78-87 (1992).
Prabhu S. S., Runger G. C., Keats J. B.: X̄ chart with adaptive sample sizes. Int. J. Prod. Res. 31, 2895-2909 (1993).
Costa A. F. B.: X̄ charts with variable sampling size. J. Qual. Technol. 26, 155-163 (1994).
ZimmerL. S. Montgomery D. C., Runger G. C.: Evaluation of a three-state adaptive sample size X̄ control chart. Int. J. Prod. Res. 36, 733-743 (1998).
Faraz, A., Saniga, E., Kazemzade, R. B.: Economic and economical statistical design of Hotelling's T2 control chart with two-state adaptive sample size. J. Stat. Comput. Simul. (2009). doi: 10. 1080/00949650903062574.
Weiler H.: On the most economical sample size for controlling the mean of a population. Ann. Math. Stat. 23, 247-254 (1952).
Girschick M. A., Rubin H.: A Bayes' approach to a quality control model. Ann. Math. Stat. 23, 114-125 (1952).
Duncan A. J.: The economic design of X̄ charts used to maintain current control of a process. J. Am. Stat. Assoc. 51, 228-242 (1956).
Lorenzen T. J., Vance L. C.: The economic design of control charts: a unified approach. Technometrics. 28, 3-11 (1986).
Montgomery D. C.: The economic design of control charts: a review and literature survey. J. Qual. Technol. 12, 75-87 (1980).
Woodall W. H.: Weaknesses of the economical design of control charts. Technometrics. 28, 408-409 (1986).
Saniga E. M.: Economic statistical control chart designs with an application to X̄ and R charts. Technometrics. 31, 313-320 (1989).
Woodall W. H., Montgomery D. C.: Research issues and ideas in statistical process control. J. Qual. Technol. 31, 376-386 (1999).
Hotelling H.: Multivariate quality control-illustrated by the air testing of sample bombsights. In: Eisenhart, C., Hastay, M. W., Wallis, W. A. (eds) Techniques of Statistical Analysis., MacGraw-Hill, New York (1947).
Lowry C. A., Montgomery D. C.: A review of multivariate control charts. IIE Trans. 27, 800-810 (1995).
Chen, Y.-K., Hsieh, K.-L.: Hotelling's T2 charts with variable sample size and control limit. Eur. J. Oper. Res. (2006). doi: 10. 1016/j. ejor. 2006. 09. 046.
Aparisi F.: Hotelling's T2 control chart with adaptive sample sizes. Int. J. Prod. Res. 34, 2853-2862 (1996).
Aparisi F., Haro C. L.: Hotelling's T2 control chart with sampling intervals. Int. J. Prod. Res. 39, 3127-3140 (2001).
Aparisi F., Haro C. L.: A comparison of T2 control charts with variable sampling schemes as opposed to MEWMA chart. Int. J. Prod. Res. 41, 2169-2182 (2003).
Faraz, A., Moghadam, M. B.: Hotelling's T2 control chart with two-state adaptive sample size. Qual. Quan. Int. J. Methodol. (2008). doi: 10. 1007/s11135-008-9167-x.
Faraz, A., Chalaki, K., Moghadam, M. B.: On the properties of the Hotelling's T2 control chart with VSI scheme. Qual. Quant. Int. J. Methodol. (2010). doi: 10. 1007/s11135-010-9314-z.
Faraz A., Parsian A.: Hotelling's T2 control chart with double warning lines. J. Stat. Pap. 47, 569-593 (2006).
Montgomery D. C., Klatt P. J.: Economic design of T2 control charts to maintain current control of a process. Manag. Sci. 19, 76-89 (1972).
Taylor H. M.: Markovian sequential replacement processes. Ann. Math. Stat. 36, 13-21 (1965).
Chou C. Y., Chen C. H., Chen C. H.: Economic design of variable sampling intervals T2 control charts using genetic algorithms. Expert Syst. Appl. 30, 233-242 (2006).
Chen, Y. K.: Economic design of variable sampling interval T2 control charts-a hybrid Markov chain approach with genetic algorithms. Expert Syst. Appl. (2006).
Chen, Y. K.: Economic design of variable T2 control chart with the VSSI sampling scheme. Qual. Quant. (2009). doi: 10. 1007/s11135-007-9101-7.
Faraz, A., Saniga, E.: Economic and Economical Statistical Design of Hotelling's T2 Control Chart with Double Warning Lines. Qual. Reliab. Eng. Int. (2010). doi: 10. 1002/qre. 1095.
