Classical and Bayesian estimation of the indexCpmkand 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.

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