Abstract
Process capability indices are important measures in statistical science and index Cpk is the most commonly used index in managerial decisions. In statistical inferences for Cpk, testing problems are relatively less explored than point and interval estimating problems. Tests for Cpk 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 Cpk that is asymptotically equivalent to the likelihood ratio test. The above results then lead to an asymptotically UMP test for Cpk. In practice, UMP test provides a wise way to reduce the risk of making wrong decisions and save resources.
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