The Performance of MCUSUM Control Charts when the Multivariate Normality Assumption Is Violated
Keywords:
MCUSUM control chart, average run length, standard deviation of run length, multivariate distributionsAbstract
A multivariate cumulative sum (MCUSUM) control chart is one type of multivariate control chart for monitoring the mean vector. A multivariate normal distribution is an important assumption that is used to describe a behavior of a set of quality characteristics of interest. This research explores the sensitivity of ARLs and SDRLs when the MVN assumption is incorrect. ARLs and SDRLs for data from multivariate uniform, beta, and lognormal distributions are estimated and compared to ARLs and SDRLs under the MVN assumption. The ratios of SDRL/ARL are also computed to consider a relationship between ARL and SDRL.
References
Crosier RB. Multivariate generalizations of cumulative sum quality-control schemes. Technometrics. 1988; 30: 291-303.
Healy JD. A note on multivariate CUSUM procedures. Technometrics. 1987; 29: 409-412.
Hofert M. On Sampling from the Multivariate Distribution. The R Journal. 2013; 5: 129-136.
Johnson NL, Kotz S, Balakrishnan N. Continuous Univariate Distributions Volume 1. 2nd edition. New York: John Wiley & Sons; 1994.
Johnson NL, Kotz S, Balakrishnan N. Continuous Univariate Distributions Volume 2. 2nd edition. New York: John Wiley & Sons; 1995.
Kotz S, Naradajah S. Multivariate t Distributions and Their Applications. Cambridge: Cambridge University Press; 2004.
Mahmoud MA, Maravelakis PE. The performance of Multivariate CUSUM control charts with estimated parameters. J Stat Comput Simulat. 2013; 83: 721-738.
Nelsen RB. An Introduction to Copulas. 2nd edition. New York: Springer; 2006.
Nidsunkid S, Borkowski JJ, Budsaba K. The effects of violations of the multivariate normality assumption in multivariate Shewhart and MEWMA control charts. Qual Reliab Eng Int. 2017; 33: 2563-2576.
Pignatiello JJ, Runger GC. Comparisons of multivariate CUSUM charts. J Qual Tech. 1990; 22: 173-186.
Rencher AC. Methods of Multivariate Analysis. 2nd edition. New York: John Wiley & Sons; 2002.
Somran S, Areepong Y, Sukparungsee S. Analytic and numerical solutions of ARLs of CUSUM procedure for exponentially distributed observations. Thail Stat. 2015; 14: 83-91.
Sukparungsee S, Kuvattana S, Busababodhin P, Areepong Y. Multivariate copulas on the MCUSUM control chart. Cogent Math. 2015; 4: 1-9.
Trivedi, PK, Zimmer DM. Copula modeling: An introduction for practitioners. Foundation and Trends in Econometrics. 2005; 1: 1-111.
Woodall WH, Ncube MM. Multivariate CUSUM quality control procedures. Technometrics. 1985; 27: 285-292.
Healy JD. A note on multivariate CUSUM procedures. Technometrics. 1987; 29: 409-412.
Hofert M. On Sampling from the Multivariate Distribution. The R Journal. 2013; 5: 129-136.
Johnson NL, Kotz S, Balakrishnan N. Continuous Univariate Distributions Volume 1. 2nd edition. New York: John Wiley & Sons; 1994.
Johnson NL, Kotz S, Balakrishnan N. Continuous Univariate Distributions Volume 2. 2nd edition. New York: John Wiley & Sons; 1995.
Kotz S, Naradajah S. Multivariate t Distributions and Their Applications. Cambridge: Cambridge University Press; 2004.
Mahmoud MA, Maravelakis PE. The performance of Multivariate CUSUM control charts with estimated parameters. J Stat Comput Simulat. 2013; 83: 721-738.
Nelsen RB. An Introduction to Copulas. 2nd edition. New York: Springer; 2006.
Nidsunkid S, Borkowski JJ, Budsaba K. The effects of violations of the multivariate normality assumption in multivariate Shewhart and MEWMA control charts. Qual Reliab Eng Int. 2017; 33: 2563-2576.
Pignatiello JJ, Runger GC. Comparisons of multivariate CUSUM charts. J Qual Tech. 1990; 22: 173-186.
Rencher AC. Methods of Multivariate Analysis. 2nd edition. New York: John Wiley & Sons; 2002.
Somran S, Areepong Y, Sukparungsee S. Analytic and numerical solutions of ARLs of CUSUM procedure for exponentially distributed observations. Thail Stat. 2015; 14: 83-91.
Sukparungsee S, Kuvattana S, Busababodhin P, Areepong Y. Multivariate copulas on the MCUSUM control chart. Cogent Math. 2015; 4: 1-9.
Trivedi, PK, Zimmer DM. Copula modeling: An introduction for practitioners. Foundation and Trends in Econometrics. 2005; 1: 1-111.
Woodall WH, Ncube MM. Multivariate CUSUM quality control procedures. Technometrics. 1985; 27: 285-292.
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Published
2018-07-19
How to Cite
Nidsunkid, S., Borkowski, J. J., & Budsaba, K. (2018). The Performance of MCUSUM Control Charts when the Multivariate Normality Assumption Is Violated. Thailand Statistician, 16(2), 140–155. Retrieved from https://ph02.tci-thaijo.org/index.php/thaistat/article/view/135559
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