Markov chain process,; Multivariate T 2 control chart; Variable sampling plan
Abstract :
[en] Recent studies have shown that the T 2 control chart with variable sampling
intervals (VSI) and/or variable sample sizes (VSS) detects process shitis faster
than the traditional T 2 chart. This article extends these studies for processes that
are monitored with VSI and VSS using double warning lines ( T 2 - DWL ). It is
assumed that the length of time the process remains in control has exponential
distribution. The properties of T 2- DWL chart are obtained using Markov
chains. The results show that the T 2 - DWL chart is quicker than VSI and/or
VSS charts in detecting almost all shifts in the process mean.
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
Parsian, Ahmad; University of Tehran, Theran, Iran > School of Mathematics, Statistics and Computer Science,
Language :
English
Title :
Hotelling's T 2 control chart with double warning lines
scite shows how a scientific paper has been cited by providing the context of the citation, a classification describing whether it supports, mentions, or contrasts the cited claim, and a label indicating in which section the citation was made.
Bibliography
Alt, F. B. (1973), Aspects of Multivariate Control Charts. M.Sc. Thesis, Georgia Institute of Technology, Atlanta, GA.
Alt, F. B. (1982), Multivariate Quality Control: State of the art. ASQC Quality Congress Transactions, 886-893.
Alt, F. B. (1985), Multivariate control charts. In Encyclopedia of statistical Science, vol. 6, S. Kotz and N.L. Johnson (eds.), New York: Wiley, 110-122.
Aparisi, F. (1996), Hotelling's T2 control chart with adaptive sample sizes, International Journal of Production Research, Vol. 34, No. 10, 2853-2862.
Aparisi, F. (2000), Sampling plans for the multivariate T2 control chart. International Journal of Production Research
Aparisi, F. and Haro, C. L. (2001), Hotelling's T2 control chart with variable sampling intervals, International Journal of Production Research, Vol. 39, No. 14, 3127-3140.
Aparisi, F. and Haro, C. L. (2003), A comparison of T2 charts with variable sampling scheme as opposed to MEWMA chart. International Journal of Production Research, Vol. 41, No. 10, 2169-2182.
Bai, D. S. and Lee, K. T. (2002), Variable sampling interval X̄ control charts with an improved switching rule. International Journal of Production Economics, Vol. 76, 189-199.
Burr, I.W. (1969), Control charts for measurements with varying sample sizes. Journal of Quality Technology, No. 1, 63-167.
Chengalur, I. N., Arnold, J. C., and Reynolds, M. R., JR. (1989), Variable sampling intervals for multi parameter Shewhart charts. Communication in Statistics: Theory and Methods, 18, 1769-1792.
Costa, A. F. B. (1994), X̄ charts with variable sampling size. Journal of Quality Technology, No. 26, 155-163.
Costa, A. F. B. (1997), X̄ charts with variable sample size and sampling intervals. Journal of Quality Technology, Vol. 29, No. 2, 197-204.
Cui, R., and Reynolds, M. R., JR. (1988), X̄-charts with runs rules and variable sampling intervals. Communications in statistics: Simulation and Computation, 17, 1073-1093.
Daudin, J. J. (1992), Double sampling ̄ charts. Journal of Quality Technology, 24, 78-87.
Hotelling, H. (1947), Multivariate quality control. In Techniques of statistical Analysis, C. Eisenhart, M. Hastay and W. A. Wallis (eds.), New York: McGraw-Hill, pp111-184.
Jackson, J. E. (1959), Quality control methods for several related variables. Technometrics, Vol. 1, No. 4, 359-377.
Jackson, J. E. (1985), Multivariate Quality Control. Communications in Statistics, Vol. 14, No. 11, 2657-2688.
Lowry, C. A., Woodall, W. H., Champ, C. W. and Rigdon, S. E. (1992), A multivariate exponentially weighted moving average control charts. Technometrics, Vol. 34, No. 1, 46-53
Molnau, W. E., Runger, G. C., Montgomery, D. C., Skinner, K.R., Loredo, E. N., and Prabhu, S. S. (2001), A program for ARL calculation for multivariate EWMA charts. Journal of Quality Technology, Vol. 33, No. 4, 515-521
Park. C. and Reynolds, M. R., JR. (1999), Economic design of a variable sampling rate X̄ -chart. Journal of Quality Technology, Vol. 31, 427-443.
Pignatiello, J. J. and Runger, G. C. (1990), Comparisons of Multivariate CUSUM Charts, Journal of Quality Technology, Vol. 22, 173-186.
Prabhu, S. S., Runger, G. C. and Keats, J. B. (1993), X̄ chart with adaptive sample sizes. International Journal of Production Research, Vol. 31, 2895-2909.
Prabhu, S. S., Montgomery, D. C. and Runger, G. C. (1994), A combined adaptive sample size and sampling interval X̄ control scheme. Journal of Quality Technology, Vol. 26, NO. 3, 164-176.
Prabhu, S. S. and Runger, G. C. (1997), Designing a Multivariate EWMA Control Chart. Journal of Quality Technology, Vol. 29, No. 1, 8-15
Reynolds, M. R., JR., and Arnold, J. C. (1989), Optimal one-sided Shewhart control charts with variable sampling intervals. Sequential Analysis, Vol. 8, 51-77.
Reynolds, M. R., JR., and Arnold, J. C. (1996), Variable sampling intervals X̄ charts in the presence of correlation. Journal of Quality technology, Vol. 28, No.2, 12-30.
Reynolds, M. R., (1996a), Shewhart and EWMA control charts using Variable sampling intervals with sampling at fixed times. Journal of Quality technology, Vol. 28, 199-212.
Reynolds, M. R., JR. (1996b), Variable sampling interval control charts with sampling at fixed times. IIE Transactions, Vol. 28, 497-510.
Reynolds, M. R. Jr. and Arnold J. C. (2001), EWMA control charts with variable sample sizes and variable sampling intervals. Vol. 33, 511-530.
Runger, G. C., and Pignatiello, J. J. (1991), Adaptive sampling for process controls. Journal of Quality Technology, Vol. 23, 135-155.
Runger, G. C., and Montgomery, D. C. (1993), Adaptive sampling enhancements for Shewhart control charts. IIE Transactions, Vol. 25, 41-51.
Runger, G. C. and Prabhu, S. S. (1996), A Markov chain model for the multivariate exponentially weighted moving average control chart. JASA,Vol. 91, No. 436, 1701-1706
Saccucci, M. S., Amin, R. W. and Lucas, J. M. (1992), Exponentially weighted moving average control schemes with variable sampling intervals. Communications in Statistics-Simulation and Computation, Vol. 21, 627-657.
Shamma, S. E., Amin, R. W. and Shamma, A. K. (1991), A double exponentially weighted moving average control procedure with variable sampling intervals. Communications in Statistics-Simulation and Computation, Vol. 20, 511-528.
Taam, W., Subbaiah, P., and Liddy, W. (1993), A note on multivariate capability indices. Journal of Applied Statistics Vol. 20, No. 3, 339-351
Zimmer, L. S., Montgomery, D. C., and Runger, G. C., (1998), Evaluation of a Three-state adaptive sample size X̄ control chart. International Journal of Production Research, Vol. 36, 733-743.
This website uses cookies to improve user experience. Read more
Save & Close
Accept all
Decline all
Show detailsHide details
Cookie declaration
About cookies
Strictly necessary
Performance
Strictly necessary cookies allow core website functionality such as user login and account management. The website cannot be used properly without strictly necessary cookies.
This cookie is used by Cookie-Script.com service to remember visitor cookie consent preferences. It is necessary for Cookie-Script.com cookie banner to work properly.
Performance cookies are used to see how visitors use the website, eg. analytics cookies. Those cookies cannot be used to directly identify a certain visitor.
Used to store the attribution information, the referrer initially used to visit the website
Cookies are small text files that are placed on your computer by websites that you visit. Websites use cookies to help users navigate efficiently and perform certain functions. Cookies that are required for the website to operate properly are allowed to be set without your permission. All other cookies need to be approved before they can be set in the browser.
You can change your consent to cookie usage at any time on our Privacy Policy page.
