基于马尔可夫链的动态故障树分析方法

The Dynamic Fault Tree Analysis Method Based on Markov Chain

对于状态较多的动态故障树(DFTA)转换为连续参数的马尔可夫链后,可以将状态转移图分解成若干条状态转移链,根据不同的链长,分别推导出概率计算公式。在应用时只要套用这些公式,然后将各条链的概率相加,便可得到DFTA的失效概率。对于给出的状态转移图,提出并证明了基于连续参数的马尔可夫链的DFTA分析的可靠性计算(解析求解)公式。与传统的方法相比,该方法可以避免直接求解微分方程的复杂运算,便于工程实际应用。

A dynamic fault tree analysis （DFTA） method based on Markov chain was proposed. Its principle is disassembling the state transform figures into several state transform chains firstly, and the chain probability formula can be got according to the length of the chains. Then the dynamic fault tree failure probability can be obtained by adding each chain probability. For the given state transform figures, the reliability analytical formula of DFTA based on the consecutive parameter Markov chain was proposed and verified. In comparison with the conventional methods, this method needn＇ t solve the differential equation, can be applied to engineering easily.