Hotelling’s T 2 control chart; Markoc chain; Adjusted average time to signal (AATS)
Abstract :
[en] When T 2 control chart is used to monitor a process, it is usually assumed that
the samples of size n0 is taken at constant intervals t0 . In this paper, we investigate the
T 2 control chart for monitoring the process mean vector when the sampling intervals are
variable. Recent studies have shown that the variable sampling interval (VSI) scheme helps
practitioners detect process shifts more quickly than the classical scheme Fixed Ratio Sampling
(FRS). In this paper, it is assumed that the length of time the process remains in control
is exponentially distributed.
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
Chalaki, Kamyar; Islamic Azad University–Urmia Branch, Urmia, Iran > School of Mathematical Science,
Moghadam, M. B.; Allameh Tabatabaee University, Tehran, Iran > Department of Statistics, Faculty of Economic,
Language :
English
Title :
On the properties of the hotelling’s T2 control chart with variable sampling intervals
Alt, F. B.: Multivariate quality control: state of the art. In: ASQC Quality Congress Transactions, pp. 886-893. (1982).
Alt F. B.: Multivariate quality control: state of the art. In: Kotz, S., Johnson, N. L. (eds) Encyclopedia of statistical science, vol. 6, pp. 110-122. Wiley, New York (1985).
Andrade J. M., Muniategui S., Prada D.: Use of multivariate techniques in quality control of kerosene production. Fuel 76(1), 51-59 (1997).
Aparisi F., Haro C. L.: Hotelling's T2 control chart with variable sampling intervals. Int. J. Prod. Res. 39(14), 3127-3140 (2001).
Bai D. S., Lee K. T.: Variable sampling interval X̄ control charts with an improved switching rule. Int. J. Prod. Econ. 76, 189-199 (2002).
Chengalur I. N., Arnold J. C., Reynolds M. R. Jr: Variable sampling intervals for multi parameter Shewhart charts. Commun. Stat.: Theory Method 18, 1769-1792 (1989).
Colon H. I. E., Gonzalez Barreto D. R.: Component registration diagnosis for printed circuit boards using process-oriented basis elements. Comp. Ind. Eng. 33(1/2), 389-392 (1997).
Costa A. F. B.: X̄ charts with variable sample size and sampling intervals. J. Qual. Technol. 29(2), 197-204 (1997).
Cui R., Reynolds M. R. Jr: X̄-charts with runs rules and variable sampling intervals. Commun. Stat.: Simul. Comput. 17, 1073-1093 (1988).
Hatton M. B.: Effective use multivariate control charts. Research publication GMR-4513, General Motors Research Lab, Warren, MI (1983).
Hotelling H.: Multivariate quality control. In: Eisenhart, C., Hastay, M., Wallis, W. A. (eds) Techniques of statistical analysis, pp. 111-184. McGraw-Hill, New York (1947).
Jackson J. E.: Multivariate quality control. Commun. Stat. 14(11), 2657-2688 (1985).
Kourti T., MacGregore J. F.: Multivariate SPC methods for process and products monitoring. J. Qual. Technol. 28(4), 409-428 (1996).
Majcen N., Rius F. X., Zupan J.: Linear and non-linear multivariate analysis in the quality control of industrial dioxide white pigment. Anal. Chim. Acta 348, 87-100 (1997).
Mason R. L., Young J. C.: Multivariate Statistical Process Control with Industrial Applications. ASA-SIAM, Philadelphia, PA (2002).
Nijhius A., deJong S., Vandeginste B. G. M.: Multivariate statistical process control in chromatography. Chemom. Intell. Lab. Syst. 38(1), 51-62 (1997).
Reynolds M. R. Jr, Arnold J. C.: Optimal one-sided Shewhart control charts with variable sampling intervals. Seq. Anal. 8, 51-77 (1989).
Reynolds M. R. Jr, Arnold J. C.: Variable sampling intervals X̄ charts in the presence of correlation. J. Qual. Technol. 28(2), 12-30 (1996).
Runger G. C., Pignatiello J. J.: Adaptive sampling for process controls. J. Qual. Technol. 23, 135-155 (1991).
Runger G. C., Montgomery D. C.: Adaptive sampling enhancements for Shewhart control charts. IIE Transac. 25, 41-51 (1993).
Ryan T. P.: Statistical Methods for Quality Improvement. Willey, INC, New York (2000).
Sullivan J. H., Woodall W. H.: A comparison of multivariate control charts for individual observations. J. Qual. Technol. 34, 260-276 (1996).
Sullivan J. H., Woodall W. H.: Adapting control charts for the preliminary analysis of multivariate observations. Commun. Stat.-Simul. Comput. 27, 953-979 (1998).
