Assessing the Lifetime Performance Index Using Exponentiated Frechet Distribution with the Progressive First-Failure-Censoring Scheme

Abstract

Process capability analysis has been widely used to monitor the performance of industrial processes. In practice, lifetime performance index C_L is a popular means to assess the performance and potential of their processes, where L is the lower specification limit. This study constructs the maximum likelihood (ML) and the Bayesian estimators of C_L for the exponentiated Frechet (EF) model with progressive first-failure-censoring scheme. These estimates are then used for constructing a confidence interval for C_L. The MLE and the Bayesian estimators of C_L are then utilized to develop a new hypothesis testing procedure in the condition of known L. Finally, we give a practical example and the Monte Carlo simulation study to illustrate the use of the testing procedure under given significance level.