Unification of some multivariate process capability indices for asymmetric specification region

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 C-M(u, v), was developed. In the present paper, we study some properties of C-M(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 C-M(u, v). Finally, the superstructure is applied to a numerical example to supplement the theory developed in this article.