Inferences of the Lifetime Performance Index with Lomax Distribution Based on Progressive Type-II Censored Data

Abstract

Effective management and the assessment of quality performance of products is important in modern enterprises. Often, the business performance is measured using the lifetime performance index CL to evaluate the potential of a process, where L is a lower specification limit. In this paper the maximum likelihood estimator (MLE) of CL is derived based on progressive Type II sampling and assuming the Lomax distribution. The MLE of CL is then utilized to develop a new hypothesis testing procedure for given value of L. Moreover, we develop the Bayes estimator of CL assuming the conjugate prior distribution and applying the squared-error loss function. The Bayes estimator of CL is then utilized to develop a credible interval again for given L. Finally, we propose a Bayesian test to assess the lifetime performance of products and give two examples and a Monte Carlo simulation to assess and compare the two ML-approach with the Bayes-approach with respect to the lifetime performance index CL.