Unification of some multivariate process capability indices for asymmetric specification region

Abstract

In manufacturing industries, it is often seen that the bilateral specification limits corresponding to a particular quality characteristic are not symmetric with respect to the stipulated target. A unified superstructure C′′ p(u, v) of univariate process capability indices was specially designed for processes with asymmetric specification limits. However, as in most of the practical situations a process consists of a number of inter-related quality characteristics, subsequently, a multivariate analogue of C′′ p(u, v), which is called CM(u, v), was developed. In the present paper, we study some properties of CM(u, v) like threshold value and compatibility with the asymmetry in loss function. We also discuss estimation procedures for plug-in estimators of some of the member indices of CM(u, v). Finally, the superstructure is applied to a numerical example to supplement the theory developed in this article.