Multivariate capability indices: Distributional and inferential properties

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.