The Evaluation on the Process Capability Index <i>C_L</i> for Exponentiated Frech’et Lifetime Product under Progressive Type I Interval Censoring

Abstract

We present the likelihood inferences on the lifetime performance index CL to evaluate the performance of lifetimes of products following the skewed Exponentiated Frech’et distribution in many manufacturing industries. This research is related to the topic of skewed Probability Distributions and Applications across Disciplines. Exponentiated Frech’et distribution is a generalization of some lifetime distributions. The maximum likelihood estimator for CL for lifetimes with exponentiated Frech’et distribution is derived to develop a computational testing procedure so that experimenters can implement it to test whether the lifetime performance reached the pre-assigned level of significance with a given lower specification limit under progressive type I interval censoring. At the end, two examples are provided to demonstrate the implementation on the algorithm for our proposed computational testing procedure.

Keywords

• progressive type I interval censoring
• lifetime performance index
• exponentiated Frech’et distribution
• maximum likelihood estimator
• hypothesis testing procedure