Classical and the Bayesian estimation of process capability index Cpy: A comparative study

In this study, to estimate the process capability index Cpy when the process follows different distributions (Lindley, Xgamma, and Akash distribution), we have used five methods of estimation, namely, the maximum likelihood method of estimation, least and weighted least squares method of estimation, maximum product of spacings method of estimation and Bayesian method of estimation. The Bayesian estimation is studied for symmetric loss function with the help of the Metropolis-Hastings algorithm method. The confidence intervals for the index Cpy are constructed based on four bootstrap methods and Bayesian methods. We studied the performances of these estimators based on their corresponding MSEs/risks for the point estimates of Cpy, and average widths AW for interval estimates. To assess the accuracy of the various approaches, Monte Carlo simulations are conducted. It is found that the Bayes estimates performed better than the considered classical estimates in terms of their corresponding risks. To illustrate the performance of the proposed methods, two real data sets are analyzed.