Multivariate Capability Indices: Distributional and Inferential Properties

Abstract

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 MC p and MC pm , to evaluate multivariate process capability. We investigate the statistical properties of the estimated MC p and obtain the lower confidence bound for MC p . We also consider testing MC p , and provide critical values for testing if a multivariate process meets the preset capability requirement. In addition, an approximate confidence interval for MC pm 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.

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