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

Authors:
Mohammad Vali Ahmadi;Mahdi Doostparast;Jafar Ahmadi
Affiliations:
-;-;-
Venue:
Journal of Computational and Applied Mathematics
Year:
2013

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Abstract

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 (C"L) proposed by Montgomery (1985) [1], is used for evaluating the performance of a process with respect to a lower specification limit (L). The maximum likelihood estimate of C"L is obtained on the basis of the progressive first-failure censored data. This estimate is then used for developing a confidence interval for C"L. The behavior of the confidence interval for the parameter C"L 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 C"L based on mean squared error (MSE) and Pitman measure of closeness (PMC) criteria is done.