Classical and Bayesian estimation of the index C_pmk and its confidence intervals for normally distributed quality characteristic

Abstract

In this article we consider the process capability index (PCI) $C_{pmk}$ which can be used for normal random variables. The objective of this article is four fold: first we address the different classical methods of estimation of the PCI $C_{pmk}$ from frequentest approaches for the normal distribution and compare them in terms of their biases and mean squared errors. Second, we compare three bootstrap confidence intervals (BCIs) of the PCI $C_{pmk}$. Third, we consider Bayesian estimation under symmetric and asymmetric loss functions. Fourth, we have incorporated a tolerance cost function in the index $C_{pmk}$ to develop a new cost effective PCI $C_{pmkc}$. A Monte Carlo simulation study has been carried out to compare the performance of the classical BCIs and highest posterior density credible intervals of PCIs $C_{pmk}$ and $C_{pmkc}$ in terms of average width and coverage probability. Finally, two real data sets have been analyzed for illustrative purposes.

Keywords:

• Process capability index
• normal distribution
• Bayesian estimation
• bootstrap confidence intervals
• cost function

Acknowledgments

The authors would like to thank the reviewers, the editor and the associate editor who helped to substantially improve the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).