Uniformly Most Powerful Test for Process Capability Index C_pk

Abstract

Process capability indices are important measures in statistical science and index C_pk is the most commonly used index in managerial decisions. In statistical inferences for C_pk, testing problems are relatively less explored than point and interval estimating problems. Tests for C_pk are often based on confidence intervals obtained from central limit theorems. Unfortunately, most tests are lack of theoretical justifications. In this article, we first propose a test for C_pk that is asymptotically equivalent to the likelihood ratio test. The above results then lead to an asymptotically UMP test for C_pk. In practice, UMP test provides a wise way to reduce the risk of making wrong decisions and save resources.

Key Words:

• Likelihood ratio test
• process capability index
• UMP test

Additional information

Notes on contributors

Sy-Mien Chen

Sy-Mien Chen Associate Professor of the Department of Mathematics, Fu-Jen Catholic University, Taiwan. She is a member of ASQ. Her research interest is industrial statistics.

Yu-Sheng Hsu

Yu-Sheng Hsu Associate Professor in the Department of Mathematics, National Central University, Taiwan. His research interests include nonparametric statistical inferences, industrial statistics and statistical inferences for stochastic processes. His research works have been published largely in statistical journals.