Conditional Confidence Intervals of the Process Capability Index Cpk

• Activity Number: 239
• Type: Contributed
• Date/Time: Monday, July 30, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Quality and Productivity Section
• Author(s): Chien-Pai Han*+ and Jianchun Zhang
• Companies: The University of Texas and The University of Texas at Arlington
• Keywords: Preliminary test ; conditional confidence interval ; process capability index ; length of interval ; coverage probability

Abstract

The process capability index Cpk involves the process mean µ and the process standard deviation s. When µ 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 µ and s separately and sequentially, instead of testing µ 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 µ and s are all unknown. An extension of the general method for finding a confidence interval of an unknown quant