基于Markov Chain Monte Carlo的幂律过程的Bayesian分析

在多种合理的无信息先验分布下,基于Markov Chain Monte Carlo方法,提出了一种简单且易于抽样的幂律过程的Bayesian分析方法.所提方法将失效、时间截尾数据统一分析,能快捷地获取幂律过程模型参数的Markov Chain Monte Carlo样本,利用该样本不但能直接给出模型参数函数的后验分布,还能给出单样预测和双样预测的分析.一个经典工程数值算例说明了所提方法的可行性、合理性与有效性.该方法具有一定的优越性,可为小子样可靠性增长分析提供一种值得参考的方法.

Bayesian analysis for the power law process based on Markov Chain Monte Carlo

Based on Markov Chain Monte Carlo technique, a simple sampling approach for the Bayesian analyses of a Power Law Process is presented under various reasonable noninformative priors. The Bayesian approach provides a unified methodology for both time and failure truncated data. Markov Chain Monte Carlo samples for the Power Law Process are easily obtained from the presented approach. Based on these MCMC samples, not only the posterior distributions of some parameter functions of the Power Law Process are given directly, but also the methodologies for single-sample and two-sample prediction are given easily. Results from an engineering numerical example illustrate the feasibility, rationality and validity of the presented approach. The proposed approach has a certain superiority, hence it provides an alternative method for the reliability growth analyses of small size of samples.