An Algebraic Binary Decision Diagram for Analysis of Dynamic Fault Tree

Dynamic fault tree (DFT) is an extension of traditional static fault tree, in which several dynamic gates are introduced to model sequential dependency between fault events. As for the quantitative analysis of DFT, sequential binary decision diagram (SBDD) has been proposed by incorporating sequential nodes into traditional binary decision diagram (BDD). With SBDD, a DFT can be reduced into a sum of disjoint products (SDP) of basic events and sequential nodes, which can avoid the space explosion problem and exponential complexity caused by traditional Markov chain and inclusion/exclusion based solutions, respectively. However, the SBDD is not developed base on a well-defined temporal or sequential algebra. Rather, it is developed based on a precedence operator with specific and very limited number of reduction rules. The applications of SBDD is thus restricted to the DFTs whose dynamic gates consist of inputs of only basic events or some specific events. In this paper, we present an algebraic binary decision diagram (ABDD) based on the algebraic framework for DFT proposed by G. Merle et al. In addition to the existing laws for the reduction of arbitrary DFT with any structure, we introduce a set of new laws for the reduction of SDP in the ABDD. Thanks to the sound algebraic framework and complete set of laws, ABDD is applicable for the analysis of general DFT without any structure restriction. We illustrate our approach and compare the difference with SBDD by several examples.