区间不确定信息下可修系统基于幂律过程的贝叶斯可靠性评估方法研究

贝叶斯方法常用于小子样场合下航空航天等领域中可修系统的可靠性评估，由于一些不确定因素影响致使无法精确收集先验信息和/或可修系统的故障信息，但却可获得其上下界信息。针对区间不确定信息情形，本文提出多台可修系统当其失效过程服从幂律过程（PLP）时的贝叶斯可靠性分析方法，将信息先验下PLP模型基于区间信息的贝叶斯分析转化为所求目标函数恰是该先验下PLP 模型传统贝叶斯分析的约束优化问题；具体工程实例对本文所提方法的可行性，有效性进行验证。结果表明：本文所提贝叶斯可靠性分析方法能够为小子样场合下，考虑不确定性因素影响时可修系统的可靠性评估问题研究提供一种值得参考的方法。

Research on Bayesian reliability evaluation method of repairable systems based on power law process under interval uncertain information

Bayesian approach is commonly used in the reliability assessment of repairable systems with small samples in fields such as aerospace. The knowledge about the informative prior and/or failure data from repairable systems may not be collected as precisely as possible due to uncertain factors, but can be obtained in terms of lower and upper bounds. For the case of such interval uncertainty information, this paper studies the Bayesian reliability analysis approach of multiple repairable systems whose failure process follow the power law process (PLP). Under the informative priors, the interval-based Bayesian posterior analysis of the PLP is essentially transformed into solving the constrained optimization problem in which the objective function is just the traditional Bayesian posterior analysis result of the PLP under the informative priors. Considering that the objective function in the constrained optimizations is complicated multiple integrals with no closed-form expressions and is highly nonlinear, the covariance matrix adaptation evolution strategy is employed to find the optimal solution of the optimization problem. Specific engineering examples verify the feasibility and effectiveness of the proposed approach. The proposed interval-based Bayesian approach of the PLP can provide a reference method for the reliability assessment of repairable systems with small samples in consideration of the influence of uncertain factors.