Multivariate capability indices: Distributional and inferential properties

W. L. Pearn, F. K. Wang*, C. H. Yen

*Corresponding author for this work

Research output: Contribution to journalJournal Article peer-review

22 Scopus citations


Process capability indices have been widely used in the manufacturing industry for measuring process reproduction capability according to manufacturing specifications. Properties of the univariate processes have been investigated extensively, but are comparatively neglected for multivariate processes where multiple dependent characteristics are involved in quality measurement. In this paper, we consider two commonly used multivariate capability indices MCp and MCpm, to evaluate multivariate process capability. We investigate the statistical properties of the estimated MCp and obtain the lower confidence bound for MCp. We also consider testing MCp, and provide critical values for testing if a multivariate process meets the preset capability requirement. In addition, an approximate confidence interval for MCpm is derived. A simulation study is conducted to ascertain the accuracy of the approximation. Three examples are presented to illustrate the applicability of the obtained results.

Original languageEnglish
Pages (from-to)941-962
Number of pages22
JournalJournal of Applied Statistics
Issue number8
StatePublished - 10 2007
Externally publishedYes


  • Critical value
  • Hypothesis testing
  • Lower confidence bound
  • Multivariate capability index


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