Distributional and Inferential Properties of Process Capability Indices

TLDR

Process capability indices are primarily viewed as indicators of the expected proportion of nonconforming items, rather than as linked to arbitrary loss functions. The paper surveys and critiques foundational concepts of process capability indices, aims to enhance understanding and interpretation of these indices, and proposes new PCI variants based on expected nonconforming proportions. The study focuses on distributional and inferential aspects of PCI methodology, surveying key concepts and proposing new indices tied to expected nonconforming proportions.

Abstract

In this paper we survey and critically comment on some basic concepts and notions relevant to the methodology dealing with process capability indices (PCI's). The emphasis is on distributional and inferential aspects. The intent is to contribute to the understanding and interpretation of these indices, if one is (unfortunately) required to use them. We regard them primarily as indicators of the expected proportion of nonconforming items, and not as having some relationship to arbitrary loss functions, as is currently the more fashionable viewpoint. New PCI's, related to the expected proportion of nonconforming items, are suggested.