Abstract
Estimating the accurate evaluation of product lifetime performance has always been a hot topic in manufacturing industry. This paper, based on the lifetime performance index, focuses on its evaluation when a lower specification limit is given. The progressive first-failure-censored data we discuss have a common log-logistic distribution. Both Bayesian and non-Bayesian method are studied. Bayes estimator of the parameters of the log-logistic distribution and the lifetime performance index are obtained using both the Lindley approximation and Monte Carlo Markov Chain methods under symmetric and asymmetric loss functions. As for interval estimation, we apply the maximum likelihood estimator to construct the asymptotic confidence intervals and the Metropolis–Hastings algorithm to establish the highest posterior density credible intervals. Moreover, we analyze a real data set for demonstrative purposes. In addition, different criteria for deciding the optimal censoring scheme have been studied.
Highlights
With the advancement of technology and the improvement of living standards, requirements for daily necessities have increased
Values of various scale parameters α and β and different sample sizes n, group sizes k, effective sample sizes m, and censored schemes ( R1, R2, · · ·, Rm ) from log-logistic distribution are used in simulation study
Our main consideration is the lifetime performance index CLX ± Zζ/2 q (CL), an indicator employed to evaluate the performance of a progress
Summary
With the advancement of technology and the improvement of living standards, requirements for daily necessities have increased. Symmetry 2020, 12, 937 allows removal of units at various stages during the lifetime test: progressive censoring is proposed in Reference [9]. The progressive first-failure censoring has the advantages of reducing trial time, saving trial resources, and removing a significant number of risky units from the trial at various stages of the life test. It has been widely used in reliability studies and several researchers; refer to References [14,15,16,17,18,19,20].
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