Classical and objective Bayesian estimation and confidence intervals of an asymmetric loss based capability index Cpmk′$\mathcal {C}^{\prime }_{pmk}$

Abstract

AbstractIn this paper, we introduce a new process capability index, based on an asymmetric loss function (linear exponential) for normal process. To estimate , we first obtain eight different classical methods of estimation and then consider objective Bayesian methods of estimation under the squared error loss function and the linear exponential loss function. Extensive simulations are carried out to investigate the performance of these estimation methods in terms of the mean squared errors. In addition, we compare the performance of four bootstrap confidence intervals and the highest posterior density interval of in terms of average width and coverage probability. Finally, three real‐data applications from electronic industries are provided for illustrative purposes.