Estimating the lifetime performance index with Weibull distribution based on progressive first-failure censoring scheme

An important topic in the manufacturing industries is the assessing of the lifetime performance. In this paper, it is supposed the lifetimes of products are independent and have a common Weibull distribution with a known shape parameter. The lifetime performance index (CLCL) proposed by Montgomery (1985) [1], is used for evaluating the performance of a process with respect to a lower specification limit (LL). The maximum likelihood estimate of CLCL is obtained on the basis of the progressive first-failure censored data. This estimate is then used for developing a confidence interval for CLCL. The behavior of the confidence interval for the parameter CLCL given a significance level is investigated and also two illustrative examples and a sensitivity analysis are given. For the exponential distribution as a special case of Weibull distribution, a comparison study for various estimates of CLCL based on mean squared error (MSE) and Pitman measure of closeness (PMC) criteria is done.