Reliability analysis of complex dynamic fault trees based on an adapted K.D. Heidtmann algorithm

Dynamic fault tree as a powerful analyzing tool is used to model systems having sequence- and function-dependent failure behaviors. The problem is how to quantify a complex dynamic fault tree where different dynamic gates coexist and are highly coupled. Existing analytical methods for analyzing dynamic fault trees are mainly Markov-based, inclusion–exclusion-based and sequential binary decision diagram–based approaches. Unfortunately, all these methods have their own shortcomings. As to the Markov-based method, it is frequently subjected to the problem of state-space explosion and only applicable for systems having components with exponential time-to-failure distributions. For the inclusion–exclusion-based method, it is often vulnerable to the problem of combinatorial explosion. As to the sequential binary decision diagram method, it cannot be directly applied to a complex dynamic fault tree where dynamic gates are highly coupled together, and its computational efficiency greatly depends on the chosen variable index. In this article, we put forward using an adapted K.D. Heidtmann algorithm to analyze the reliability of a complex dynamic fault tree. To improve the computational efficiency of our proposed method, products are ordered according to their lengths and compositions. To illustrate the applicability and advantages of the proposed method, a case study is analyzed. The results show the proposed method is reasonable and efficient.