Dynamic fault tree analysis based on pivotal decomposition of the structure function

Many fault-tolerant systems in real life are involved in sequence- and function-dependent failure behaviors, in which the failure of these systems depends not only on the combination of basic events, but also on their failure orders. Dynamic fault tree (DFT) as an extension of the conventional static fault tree is widely used to model such systems. The existing analytical approaches for reliability evaluation of DFT are mainly Markov-based, Inclusion-exclusion-based and sequential-BDD - based methods. Those approaches either suffer from the problem of state-space explosion or are subjected to combinatorial explosion knot or have small flaws. To overcome the shortcomings of the existing methods, a pivotal decomposition scheme upon the structure function of a given DFT is proposed in this paper. The proposed approach rewrites the structure function into equivalent sum-of-disjoint products based on Shannon decomposition theorem and exactly calculates the unreliability of non-repairable dynamic systems modeled by DFT. In addition, the proposed method is efficient compared with existing approaches. The application and advantages of the proposed method are demonstrated by analysis of a case study.