A new probability-based multivariate process capability index

Multivariate process capability indices (MPCIs) MCp, MCpk and MCpm have been proposed in literature to measure multivariate process capability. From a practitioner's view, the intention of this paper is to propose a new probability-based MPCI MSpmk which takes into account process variability, departure of the process mean from target and proportion of conformity when assessing multivariate process performance. The MSpmk is the extension in multivariate setup of univariate process capability index Spmk. The Spmk is smooth version of widely used univariate process capability index Cpmk. The MSpmk is very easy to compute and combines the merits of MPCIs MCp, MCpk and MCpm. Proposed MPCI assumes that production process is multivariate normal and specification region is rectangular. Proposed MPCI is recommendable with respect to its performance in various scenarios and its natural estimator statistical properties for real world usage.