Maximum multivariate cumulative sum (Max-MCUSUM) is one of the single control charts that plot single statistic as a representation of mean vector and covariance matrix. The Max-MCUSUM statistic has unknown specific distribution. The objective of this paper is to propose bootstrap-based Max-MCUSUM control chart for which reference value is predetermined in Phase I monitoring process. For various numbers of quality characteristics and correlation coefficients, the control limits estimated using bootstrap approach are presented in this paper. Furthermore, the average run lengths of bootstrap-based Max-MCUSUM control chart prove that the proposed control chart tends to be effective for monitoring the small shift in both mean and variance of a process. The illustrative examples are provided to demonstrate the applications of the proposed control chart for both simulation and real data.

Original languageEnglish
Pages (from-to)52-74
Number of pages23
JournalQuality Technology and Quantitative Management
Issue number1
Publication statusPublished - 2 Jan 2020


  • Average run length
  • bootstrap
  • maximum multivariate CUSUM
  • reference value
  • single control chart


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