Inferences on the lifetime performance index for Weibull distribution based on censored observations using the max p-value method

Abstract

In the service (or manufacturing) industries, process capability indices (PCIs) are utilised to assess whether product quality meets the required level. And the lifetime performance index (or larger-the-better PCI) CL is frequently used as a means of measuring product performance, where L is the lower specification limit. Hence, this study first uses the max p-value method to select the optimum value of the shape parameter β of the Weibull distribution and β is given. Second, we also construct the maximum likelihood estimator (MLE) of CL based on the type II right‐censored sample from the Weibull distribution. The MLE of CL is then utilised to develop a novel hypothesis testing procedure provided that L is known. Finally, we give one practical example to illustrate the use of the testing procedure under given significance level α.