Bayesian Inference of δ = P(X < Y) for Burr Type XII distribution based on progressively first failure-censored samples
學年 108
學期 1
出版（發表）日期 2019-09-01
作品名稱 Bayesian Inference of δ = P(X < Y) for Burr Type XII distribution based on progressively first failure-censored samples
作品名稱（其他語言）
著者 Jessie Marie Byrnes; Yu-Jau Lin; Tzong-Ru Tsai; Yuhlong Lio
單位
出版者
著錄名稱、卷期、頁數 Mathematics 7(9), 794(24 pages)
摘要 Let X and Y follow two independent Burr type XII distributions and δ=P(X<Y) . If X is the stress that is applied to a certain component and Y is the strength to sustain the stress, then δ is called the stress–strength parameter. In this study, The Bayes estimator of δ is investigated based on a progressively first failure-censored sample. Because of computation complexity and no closed form for the estimator as well as posterior distributions, the Markov Chain Monte Carlo procedure using the Metropolis–Hastings algorithm via Gibbs sampling is built to collect a random sample of δ via the joint distribution of the progressively first failure-censored sample and random parameters and the empirical distribution of this collected sample is used to estimate the posterior distribution of δ . Then, the Bayes estimates of δ using the square error, absolute error, and linear exponential error loss functions are obtained and the credible interval of δ is constructed using the empirical distribution. An intensive simulation study is conducted to investigate the performance of these three types of Bayes estimates and the coverage probabilities and average lengths of the credible interval of δ . Moreover, the performance of the Bayes estimates is compared with the maximum likelihood estimates. The Internet of Things and a numerical example about the miles-to-failure of vehicle components for reliability evaluation are provided for application purposes.
關鍵字 gibbs sampling;Markov Chain Monte Carlo;maximum likelihood estimation;Metropolis–Hastings algorithm;progressive first failure-censoring scheme
語言 en
ISSN 2227-7390
期刊性質 國外
收錄於 SCI Scopus
產學合作
通訊作者 Tzong-Ru Tsai
審稿制度 是
國別 CHE
公開徵稿
出版型式 ,電子版
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