多状态系统的动态可靠性度量及重要度分析

Dynamic Reliability Metric and Importance Analysis of Multi-State Systems

为有效表征性能退化条件下多状态系统的可靠性,确定各组件(状态)对系统的影响,文中对性能状态进行分析,提出了新的动态可靠性度量指标和性能水平限制下的重要度计算方法.首先,针对多状态系统马尔可夫过程的组合爆炸问题,应用通用生成函数法求解系统(组件)各状态的概率和可靠度、性能状态期望值、性能状态平均期望值和性能状态驻留时间长度等4种动态可靠性度量指标.然后,为满足系统(组件)的不同性能需求,综合评估各组件(状态)对系统的影响,用性能期望值定义了给定性能水平下的Birnbaum重要度、Fussell-Vesely重要度、风险业绩值和风险降低值.四缸柴油机燃油供给系统的实例结果表明,文中方法既可准确地求解系统及其组件(油泵和喷油阀)的性能状态概率,以及性能退化条件下各性能状态的可靠度、期望值、平均期望值和驻留时间长度,又能根据性能水平限制下的4种重要度综合评估各性能状态及组件对系统的影响,有助于识别出系统最薄弱的环节,提高系统可靠性.

In order to characterize the reliability of multi-state system in performance degradation condition effec-tively and determine the effects of each component （state） on the system, this paper makes a performance state analysis and presents dynamic reliability metrics as well as an importance calculation method considering perfor-mance level restrictions. Firstly, the failure probability, reliability, performance state expectation, average per-formance state expectation and performance state duration of system （ component） are calculated by using the uni-versal generating function to avoid the combinatorial explosion of Markov model in multi-state system. Then, four importance indexes under certain performance level restrictions, namely Birnbaum importance, Fussell-Vesely im-portance ,risk assessment worth and risk reduction worth, are defined with performance expectation value to com-prehensively evaluate the effects of each component （ state） on the system and meet different performance require-ments of system （component） . The application results to the fuel supply system of four-cylinder diesel engine indi-cate that the proposed approach can not only accurately solve the failure probability, reliability, performance state expectation, average performance state expectation and performance state duration of system （ component） , but also comprehensively assess the effects of each component （state） on the system according to the four importance values under performance level restrictions. Therefore, it helps improve system reliability through identifying the weakest parts in the system.