Inferences on the performance index of Weibull distribution based on k-record values

Abstract

Process capability indices are used to measure the performance of a process in the manufacturing industry. This paper derives inferences for the lifetime performance index using k-record values when the lifetime of products has a Weibull distribution. The UMVUE, an exact test and a classical confidence interval are proposed for this index when the shape parameter of Weibull distribution is known. With unknown shape parameter, a generalized confidence interval and two Bayesian confidence intervals are given. Also, it is estimated by the maximum likelihood and Bayesian estimators as well as a generalized approach. Based on the concept of generalized test variable, a generalized p-value is derived for testing the lifetime performance index. The behaviour of the proposed approaches are evaluated using Monte Carlo simulation. An illustration is given to demonstrate the proposed approaches. We also explain that the results can be utilized when the lifetime of products has an extreme value distribution.