Multivariate control charts based on the James-Stein estimator

Hsiuying Wang*, Longcheen Huwang, Jeng Hung Yu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


In this study, we focus on improving parameter estimation in Phase I study to construct more accurate Phase II control limits for monitoring multivariate quality characteristics. For a multivariate normal distribution with unknown mean vector, the usual mean estimator is known to be inadmissible under the squared error loss function when the dimension of the variables is greater than 2. Shrinkage estimators, such as the James-Stein estimators, are shown to have better performance than the conventional estimators in the literature. We utilize the James-Stein estimators to improve the Phase I parameter estimation. Multivariate control limits for the Phase II monitoring based on the improved estimators are proposed in this study. The resulting control charts, JS-type charts, are shown to have substantial performance improvement over the existing ones.

Original languageEnglish
Pages (from-to)119-127
Number of pages9
JournalEuropean Journal of Operational Research
Issue number1
StatePublished - 1 Oct 2015


  • Average run length
  • Control chart
  • James-Stein estimator
  • Multivariate normal distribution


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