Asymptotic and Bootstrap Confidence Intervals for the Process Capability Index c_py Based on Lindley Distributed Quality Characteristic

SYNOPTIC ABSTRACT

Process capability indices (PCIs) have been widely applied in measuring product potential and performance. It is of great significance to quality control engineers, as it quantifies the relation between the actual performance of the process and the preset specifications of the product. Among the plethora of the suggested PCIs, most of them were developed for normally distributed processes. In this article, we consider generalized process capability index C_py suggested by Maiti et al. (2010), which can be used for normal, non-normal, and continuous as well as discrete random variables. The objective of this article is twofold. First, we obtain maximum likelihood estimator (MLE) and minimum variance unbiased estimator (MVUE) of the PCI C_py for the Lindley distributed quality characteristics. Second, we compare asymptotic confidence interval (ACI) with four bootstrap confidence intervals (BCIs); namely, standard bootstrap (s-boot), percentile bootstrap (p-boot), Student’s t bootstrap (t-boot), and bias-corrected accelerated bootstrap (BC_a-boot) of C_py based on maximum likelihood method of estimation. Monte Carlo simulations have been carried out to compare the performance of MLEs and MVUEs, and also investigate the average widths, coverage probabilities, and relative coverages of ACI and BCIs of C_py. Two real data sets have been analyzed for illustrative purposes.

KEY WORDS AND PHRASES:

• Process capability index
• generalized process capability index
• maximum likelihood estimate
• minimum variance unbiased estimate
• asymptotic confidence interval
• bootstrap confidence intervals
• Lindley distribution

Acknowledgements

The authors would like to thank the reviewer(s) and the Editor for several helpful comments, which improved the earlier versions of this work.