Impact of multivariate normality assumption on multivariate process capability indices

Abstract

Process Capability Index (PCI) is a very popular tool for assessing performance of processes (often involving a single quality characteristic). Multivariate process capability indices (MPCI) are comparatively new to the literature and hence often involve some difficulties in practical applications. One such hurdle is multivariate normality assumption of the underlying distribution of the quality characteristics. While such assumption gives some computational as well as theoretical advantage in formulating MPCIs, often data encountered in practice do not follow multivariate normal distribution due to several reasons. Consequently, the computed values of the MPCIs may give misleading results. In the present article, we have made performance analysis of some MPCIs in the light of a dataset which has been widely used in the literature, particularly in the context of MPCIs. Most of these MPCIs were already applied to the said data in the literature and our objective is to make their comparative performance analysis. In this context, the data, though actually non-normal, is often concluded as multivariate normal by several researchers. Therefore, while making the performance analysis of the MPCIs, this aspect has also been incorporated to put emphasis on the importance of distributional assumption in a multivariate process capability analysis.

Keywords:

• Capability Index
• multivariate non-normal distribution
• multivariate normal distribution
• multivariate process quality control
• test for multivariate normality

Acknowledgement

The author is extremely thankful to the learned reviewer(s) for their valuable comments and suggestions in improving the quality of the paper.