Bootstrap confidence intervals of process capability index S_(pmk) using different methods of estimation

摘要

In this article, we propose eight different methods of estimation to estimate the unknown parameters and the PCI Spmk for the log-logistic distribution from the frequentist point of view. Next, we consider three bootstrap confidence intervals namely, standard bootstrap, percentile bootstrap and student?s t bootstrap for obtaining confidence intervals of the PCI Spmk using the aforementioned methods of estimation. Monte Carlo simulations are performed to compare the performances of coverage probabilities, average widths and relative coverage of the bootstrap confidence intervals using the proposed methods of estimation for both small and moderate samples. Besides, we have incorporated tolerance cost function in the index Spmk to develop a new cost effective PCI Spmkc. Additionally, the performances of the estimators have been compared in terms of their mean squared error using simulated samples. Finally, two real data sets are analyzed for illustrative purposes.