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

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.