Conditional Confidence Intervals of the Normal Variance and Its Application to the Process Capability Index Cp

• Activity Number: 513
• Type: Contributed
• Date/Time: Wednesday, August 3, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Chien-Pai Han*+ and Jianchun Zhang
• Companies: The University of Texas at Arlington and The University of Texas at Arlington
• Keywords: conditional confidence interval of variance ; preliminary test ; coverage probability ; process capability index Cp

Abstract

Constructing confidence intervals for the normal variance is an important inference procedure. When the experimenter has prior information about the variance, it is advantageous to use the prior information. When the experimenter is uncertain about the prior information, a preliminary test can be used to verify the validity of the information. We consider the construction of a conditional confidence interval for the variance after the rejection of the null hypothesis that the population variance is greater than or equal to a given prior value. Comparisons of the conditional confidence intervals and unconditional confidence intervals are made and the conditional coverage probabilities of the unconditional confidence intervals are investigated. Since the process capability index Cp involves only one parameter that is the process standard deviation, the conditional confidence interval for Cp can also be similarly obtained.