Assessing the process capability index for non-normal processes

In recent decades, the concept of process capability has emerged to provide a quantified prediction of process adequacy. Capability indexes have become a popular means of describing the ability of a process to produce products that meet certain specifications. These indexes provide numerical measures on process potential and performance. We consider the large-sample estimation of a capability process index. We also consider a multi-sample set up when random samples are taken from arbitrary populations. In this article, we propose shrinkage estimation strategies for estimating the population capability indexes. The classical estimator is investigated as a competitor of the proposed estimators. We also assess their properties both theoretically and numerically. An over-riding theme of this paper is that the shrinkage method provides a powerful extension of its classical counterpart for nonnormal populations.