Parametric and non-parametric bootstrap confidence intervals of C_Npk for exponential power distribution

Abstract

For enhancing the quality and productivity, the use of process capability index (PCI) has become significant in statistical process control, designed to quantify the relation between the actual performance of the process and its specified requirements. Confidence interval is an important part of PCI because it is an estimated value and provides much more information about the population characteristic of interest than does a point estimate. In this article, bootstrap confidence intervals of non-normal PCI , is studied through simulation when the underlying distribution is exponential power distribution. Maximum likelihood method is used to estimate the parameters of the model. Four (parametric as well as non-parametric) bootstrap confidence intervals, namely standard bootstrap (s-boot), percentile bootstrap (p-boot), Student’s t bootstrap (t-boot), and bias-corrected percentile bootstrap (-boot), are considered for obtaining confidence intervals of . A Monte Carlo simulation has been used to investigate the estimated coverage probabilities and average widths of the bootstrap confidence intervals. Simulation results showed that among these (s-boot, p-boot, t-boot, and -boot) confidence intervals, the performances of the s-boot confidence intervals is the best in terms of overage probabilities. Finally, three real data-sets are analyzed for illustrative purposes.

Keywords:

• Maximum likelihood estimator
• parametric bootstrap
• non-parametric bootstrap
• process capability index

Acknowledgements

The authors would like to thank the Referees, Editor-in-Chief, and Associate Editor for careful reading and for comments which greatly improved the paper. Also authors would like to thank the Assistant Librarian, Central University of Rajasthan for his valuable support.

Notes

No potential conflict of interest was reported by the authors.