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) C_L 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 C_L based on the type II right‐censored sample from the Weibull distribution. The MLE of C_L 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.

Keywords:

• product performance
• type II right censored sample
• Weibull distribution
• testing procedure
• maximum likelihood estimator

Acknowledgement

The author wish to thank the referees for their valuable suggestions which led to the improvement of this article.