Bootstrap confidence intervals of process capability indices Spmk, Spmkc and Cs for Frechet distribution

Abstract

AbstractIn this paper, we considered the Bayesian estimators under reference and Jeffery's priors and maximum likelihood estimators to estimate the unknown parameters of the process capability indices Spmk, Spmkc, and Cs for Frechet distribution. Further, we developed bootstrap confidence intervals for aforementioned process capability indices based on above‐mentioned estimators. Monte Carlo simulations are performed to investigate the performance of process capability indices through skewness, kurtosis, mean square error and widths of bootstrap confidence intervals for small, moderate, and large sample sizes. Simulations results indicate that the Bayesian estimator under reference prior outperforms even in small sample sizes, and all performed equally well for larger sample sizes. Moreover, the average width for bootstrap confidence interval for Cs is least in all. Finally, real data is analyzed for illustration purposes.