The Performance of MCUSUM Control Charts when the Multivariate Normality Assumption Is Violated

  • Sudarat Nidsunkid Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Pathum Thani 12121, Thailand.
  • John J. Borkowski Department of Mathematical Sciences, Montana State University, Bozeman, MT, 59717, USA.
  • Kamon Budsaba Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Pathum Thani 12121, Thailand.
Keywords: MCUSUM control chart, average run length, standard deviation of run length, multivariate distributions

Abstract

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.

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Published
2018-07-19
Section
Articles