Reliability analysis of non-repairable systems modeled by dynamic fault trees with priority AND gates

Many real-life systems are typically involved in sequence-dependent failure behaviors. Such systems can be modeled by dynamic fault trees DFTs with priority AND gates, in which the occurrence of the top events depends on not only combinations of basic events but also their failure sequences. To the author's knowledge, the existing methods for reliability assessment of DFTs with priority AND gates are mainly Markov-state-space-based, inclusion-exclusion-based, Monte Carlo simulation-based, or sequential binary decision diagram-based approaches. Unfortunately, all these methods have their shortcomings. They either suffer the problem of state space explosion or are restricted to exponential components time-to-failure distributions or need a long computation time to obtain a solution with a high accuracy. In this article, a novel method based on dynamic binary decision tree DBDT is first proposed. To build the DBDT model of a given DFT, we present an adapted format of the traditional Shannon's decomposition theorem. Considering that the chosen variable index has a great effect on the final scale of disjoint calculable cut sequences generated from a built DBDT, which to some extent determines the computational efficiency of the proposed method, some heuristic branching rules are presented. To validate our proposed method, a case study is analyzed. The results indicate that the proposed method is reasonable and efficient. Copyright © 2015 John Wiley & Sons, Ltd.