Confidence Intervals of a Loss Based PCI Spmk′ Using Exponentiated-Exponential Distributed Quality Characteristics

Abstract

Process capability indices (PCIs) are most effective devices/techniques used in industries for determining the quality of products and performance of manufacturing processes. In this article, we consider the process capability index $S_{\mathit{pmk}}^{\prime }$ which is based on an asymmetric loss function (linear exponential) and is applicable to normally as well as non-normally distributed processes. In order to estimate the PCI $S_{\mathit{pmk}}^{\prime }$ when the process follows exponentiated exponential distribution, we have used ten classical methods of estimation and the performances of these classical estimates for the index $S_{\mathit{pmk}}^{\prime }$ are compared in terms of mean squared errors (MSEs) through simulation study. Also, the confidence intervals for the index $S_{\mathit{pmk}}^{\prime }$ are constructed based on four bootstrap confidence interval (BCIs) methods. A simulation study is performed in order to compare the performance of these four BCIs in terms of average width and coverage probabilities. We use two published data sets related to electronic and food industries to illustrate the performance of the proposed methods of estimation and BCIs. All the data sets show that width of bias-corrected accelerated bootstrap interval is the lowest among all other considered BCIs.

KEYWORDS AND PHRASES:

• Bootstrap confidence intervals
• maximum likelihood estimator
• maximum product spacing estimator
• process capability index

Acknowledgements

The authors would like to thank to the Reviewer(s) and the Editor for several helpful comments which had improved the earlier versions of the manuscript.

Conflicts of Interest

The authors declare that they have no conflicts of interest.