基于威布尔分布多部件应力–强度模型的贝叶斯推断

Bayesian Inference for Multicomponent Stress-Strength Model under Weibull Distribution

本文考虑了一个多部件应力–强度模型的可靠性,该模型包括一个应力和多个强度的串联系统.当应力和强度变量服从相同形状参数的威布尔分布时,推导了参数的Jeffreys先验,并给出基于该先验时后验适当性的充要条件.利用Lindley近似和马尔可夫链蒙特卡罗方法对系统可靠性进行估计.通过蒙特卡罗仿真对所提方法进行评估.仿真结果表明,贝叶斯方法要优于极大似然方法,且在小样本情形下尤为突出.最后,以实际数据集为例进行了说明.

This study considers the reliability of a multicomponent stress-strength model involving one stress and multiple strengths from a series system.We derive the Jeffreys prior when the stress and strength variables follow Weibull distribution with a common shape parameter.The necessary and sufficient conditions of the propriety of the posterior distribution based on the Jeffreys prior are obtained.Lindley’s approximation and Markov chain Monte Carlo method are presented to obtain the estimates of the system reliability.The performance of the proposed methods is evaluated by Monte Carlo simulation.The simulation results show the Bayesian method outperforms maximum likelihood method,especially in the case of a small sample size.Finally,a real dataset is analyzed for illustration.