A study of multivariate (X̄, S) control chart based on Kullback-Leibler information

Yasuhiko Takemoto, Ikuo Arizono

Research output: Contribution to journalArticle

9 Citations (Scopus)


Recently, Chou et al. have considered the multivariate control chart for monitoring the process mean vector and covariance matrix for the related quality characteristics simultaneously by using log-likelihood ratio statistics. They have computed the approximation formula described with Bernoulli polynomials of degrees r≥30 by using software MATHEMATICA 4.0 for obtaining the control limit with sufficient accuracy for the specified type I error probability in the chart. However, they cannot have obtained the approximation formula for the power evaluation. By the way, Kanagawa et al. have proposed the (x̄, s)control chart for monitoring the mean and variance simultaneously based on Kullback-Leibler information when quality characteristics obey a univariate normal distribution. In this article, by adopting the procedure by Kanagawa et al., we propose the other approximation formula for determining simply the control limit with sufficient accuracy for the specified type I error probability. Furthermore, the power evaluation for the chart is also considered in theory.

Original languageEnglish
Pages (from-to)1205-1210
Number of pages6
JournalInternational Journal of Advanced Manufacturing Technology
Issue number11-12
Publication statusPublished - Jun 2005
Externally publishedYes



  • (x̄, s)control chart
  • Covariance matrix
  • Kullback-Leibler information
  • Likelihood ratio statistic
  • Mean vector
  • Multivariate statistical control charts

ASJC Scopus subject areas

  • Industrial and Manufacturing Engineering

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