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    题名: Accelerated life test method for the doubly truncated Burr type XII distribution
    作者: Xin, Hua;Liu, Zhifang;Lio, Yuhlong;Tsai, Tzong-Ru
    关键词: accelerated life test;Burr type XII distribution;Markov chain Monte Carlo;maximum likelihood estimation;Newton–Raphson method
    日期: 2020-01-23
    上传时间: 2020-07-09 12:10:23 (UTC+8)
    出版者: M D P I AG
    摘要: The Burr type XII (BurrXII) distribution is very flexible for modeling and has earned much attention in the past few decades. In this study, the maximum likelihood estimation method and two Bayesian estimation procedures are investigated based on constant-stress accelerated life test (ALT) samples, which are obtained from the doubly truncated three-parameter BurrXII distribution. Because computational difficulty occurs for maximum likelihood estimation method, two Bayesian procedures are suggested to estimate model parameters and lifetime quantiles under the normal use condition. A Markov Chain Monte Carlo approach using the Metropolis–Hastings algorithm via Gibbs sampling is built to obtain Bayes estimators of the model parameters and to construct credible intervals. The proposed Bayesian estimation procedures are simple for practical use, and the obtained Bayes estimates are reliable for evaluating the reliability of lifetime products based on ALT samples. Monte Carlo simulations were conducted to evaluate the performance of these two Bayesian estimation procedures. Simulation results show that the second Bayesian estimation procedure outperforms the first Bayesian estimation procedure in terms of bias and mean squared error when users do not have sufficient knowledge to set up hyperparameters in the prior distributions. Finally, a numerical example about oil-well pumps is used for illustration.
    關聯: Mathematics 8(2), 162
    DOI: 10.3390/math8020162
    显示于类别:[統計學系暨研究所] 期刊論文


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