Inferences on the lifetime performance index of products with Pareto distribution under progressive first-failure censored data

Inferences on the lifetime performance index of products with Pareto distribution under progressive first-failure censored data

One of the most important topics in the manufacturing industries is the evaluating the lifetime performance of products. In this paper. based on lifetime performance index C proposed by Montgomery (1985 we tackle to assess the performance of a process in the condition of known lower specification limit L. Also, it is assumed that the lifetime of products follows a common Pareto distribution with known scale parameter. On the basis of the progressive first-failure censored data, the maximum likelihood (ML) estimate of C, the uniformly most powerful (UMP) test for testing He : C S C versus H1 : Ci > C and then the uniformly most accurate (U ) lower bound for CL are obtained. In addition, based on Bayesian approach the Bayes Estimates of C. under linear-exponential (LINIEX) and squared error (SE) loss functions are derived. Finally, these Bayes estimates are utilized to develop a lower credible bound for Ct. and a Bayesian rejection region for testing Ho against H1.