Bootstrap confidence intervals of process capability indices Cpy and CNpmk using different methods of estimation for Frechet distribution

Process capability analysis is the statistical evaluation of process capability to examine how well it meets or exceeds the customers satisfaction. In present work, we are intended to evaluate two critical metrics for process quality assessment, C py and C Npmk for asymmetric Frechet distribution using different classical estimation methods namely: maximum likelihood, least squares, weighted least squares, Cramer-von-Mises, Anderson-Darling, right-tail Anderson-Darling, along Bayesian estimation using reference and Jeffreys priors. Furthermore, Monte Carlo simulations are conducted for comparative analysis of aforementioned estimation methods, using mean squared error and width of bootstrap confidence intervals. Comparative analysis demonstrates that Bayesian estimation using reference prior consistently producing smaller coefficient of mean squared errors and reduced width of bootstrap intervals for small to moderately large sample sizes. Moreover, the real data analysis is also validating the advantages of Bayesian estimations for process capability analysis.