Assessing lifetime performance index of Weibull distributed products using progressive type II right censored samples

Abstract

An important subject of discourse in manufacturing industries is the assessing of the lifetime performance index. If the lifetime of an item/product is characterized by a random variable X and considered to be satisfactory and if X exceeds a given lower specification limit, say L, then the probability of a satisfactory item is defined as $P_{r} = P(X \ge L)$, called the conforming rate. In manufacturing industries, the lifetime performance index, say $C_{L}$, proposed by Montgomery (Introduction to statistical quality control. Wiley, New York, 1985), is used to measure the performance of the product. There exists a relationship between the conforming rate ($P_{r}$) and the lifetime performance index ($C_{L}$) when the random variable X follows a parametric distribution. Henceforth, we use $C_{L}$ instead of $P_{r}$ because it is widely used in manufacturing industries as a process capability index. This study constructs various point and interval estimators of the lifetime performance index based on progressive type II right censored data for Weibull distribution with respect to both classical and Bayesian set up. Further, hypothesis testing problems concerning $C_{L}$ are proposed. We perform Monte Carlo simulations to compare the performances of the Maximum likelihood and Bayes estimates of $C_{L}$ under different censoring schemes. Finally, the potentiality of the model is analyzed by means of a real data set and a simulated sample.