Multivariate statistical process control charts based on the approximate sequential χ2 test

J. Kim, K. N. Al-Khalifa, M. K. Jeong, A. M.S. Hamouda, E. A. Elsayed

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


Similar to the univariate CUSUM chart, a multivariate CUSUM (MCUSUM) chart can be designed to detect a particular size of the mean shift optimally based on the scheme of a sequential likelihood ratio test for the noncentrality parameter. However, in multivariate case, the probability ratio of a sequential test is intractable mathematically and the test statistic based on the ratio does not have a closed form expression which makes it impractical for real application. We drive an approximate log-likelihood ratio and propose a multivariate statistical process control chart based on a sequential χ2 test to detect a change in the noncentrality parameter. The statistical properties of the proposed test statistic are explored. The average runs length (ARL) performance of the proposed charts is compared with other MCUSUM charts for process mean monitoring. The experimental results reveal that the proposed charts achieve superior, both zero-state and steady-state, ARL performance over a wide range of mean shifts, especially when the dimension of measurements is large.

Original languageEnglish (US)
Pages (from-to)5514-5527
Number of pages14
JournalInternational Journal of Production Research
Issue number18
StatePublished - Sep 17 2014

All Science Journal Classification (ASJC) codes

  • Strategy and Management
  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering


  • likelihood ratio test


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