机械系统的Bayes可靠性评估

讨论了机械系统的Ｂａｙｅｓ可靠性评估问题，当应力、强度均服从正态分布，且分布参数未知的情况下，首先分析了机械产品单元可靠性评估问题，讨论了给定验前分布情况下的单元可靠性Ｂａｙｅｓ精确下限，给出了无验前信息时的可靠性Ｂａｙｅｓ精确下限，鉴于精确限计算的复杂性，给出了应力－强度模型可靠性下限的近似计算方法，同时给出了可靠性的近似分布，然后把机械单元的可靠性信息折合到机械系统上，利用最大熵方法得到了系统可靠的验前分布，若没有做系统的可靠性试验，则根据此验前分布就可以对机械系统的可行性进行评估；若做了系统级可靠性试验，则利用Ｂａｙｅｓ公式求得系统可靠的验后分布，然后利用验后分布进行可靠评估，仿真实例说明机械系统Ｂａｙｅｓ可靠性评估的应用。

BAYESIAN RELIABILITY EVALUATION OF MECHANICAL SYSTEM

Bayesian reliability evaluation of the mechanical system is discussed. First, the reliability evaluation of mechanical components is analyzed when the stress and strength are independent and follow normal distributions. Given the prior distribution, accurate Bayesian lower bounds of the reliability of the components are discussed. Besides, accurate Bayesian lower bounds of reliability are given when none of prior information is available. Because of the complexity of calculating accurate lower bounds, the approximate methods are given to calculate the components' reliability lower bounds of a stress strength model. At the same time, the approximate distribution of the reliability of the components is given. Then the reliability information of mechanical components is converted into the mechanical system. The prior distribution of system reliability is obtained using the principle of maximum entropy. The reliability of the mechanical system is evaluated basing on the prior distribution if there are no testing data on the system. If there are testing data on the system itself, we can obtain the posterior distribution of the reliability of the system using Bayes theorem, thus we can analyze the reliability of the system basing on the posterior distribution. The simulation shows the method's application.