Parametric Confidence Intervals of S_pmk for Generalized Exponential Distribution

Abstract

The objective of this article is to compare highest posterior density (HPD) credible interval with three bootstrap confidence intervals (BCIs) as well as with asymptotic confidence interval (ACI) using maximum likelihood and Bayesian approaches of a new process capability index, S_pmk when the underlying distribution is generalized exponential. This new index can be used for normal as well as non-normal quality characteristics. Through extensive simulation studies and with two real life examples related to industry data, we compare the performances of classical and the Bayes estimates based on different loss functions and compared among the HPD credible intervals, three BCIs and ACIs in terms of coverage probabilities, average width, and respective relative coverages of the index S_pmk, respectively.

Keywords and Phrases:

• Bootstrap methods
• Chen & Ding index
• generalized exponential distribution
• process capability index

Acknowledgment

The authors would like to thank the Editor-in-Chief, Associate editor, and the referees for their insightful comments that have led to a substantial improvement to an earlier version of the paper.