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239 – Advances in Statistical Process Control

Conditional Confidence Intervals of the Process Capability Index Cpk

Sponsor: Quality and Productivity Section
Keywords: Preliminary test, conditional confidence interval, process capability index, length of interval, coverage probability

Chien-Pai Han

The University of Texas

Jianchun Zhang

The University of Texas at Arlington

The process capability index Cpk involves the process mean and the process standard deviation s. When and s are unknown we can estimate them by a random sample. When we have uncertain prior information about their values, we may check the uncertain prior information by preliminary tests. Then we can construct a conditional confidence interval of the process capability index Cpk following rejection of the preliminary tests. In this paper, we adopt two tests for testing and s separately and sequentially, instead of testing and s jointly. Conditional confidence intervals of Cpk following different results of the two tests are provided. For the case that both of the two null hypotheses are rejected, we construct the confidence interval of Cpk for which the two parameters and s are all unknown.

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