A Hierarchical Approach for Dynamic Fault Trees Solution Through Semi-Markov Process

Dynamic fault tree (DFT) is a top-down deductive technique extended to model systems with complex failure behaviors and interactions. In two last decades, different methods have been applied to improve its capabilities, such as computational complexity reduction, modularization, intricate failure distribution, and reconfiguration. This paper uses semi-Markov process (SMP) theorem for DFT solution with the motivation of obviating the model state-explosion, considering nonexponential failure distribution through a hierarchical solution. In addition, in the proposed method, a universal SMP for static and dynamic gates is introduced, which can generalize dynamic behaviors like functional dependencies, sequences, priorities, and spares in a single model. The efficiency of the method regarding precision and competitiveness with commercial tools, repeated events consideration, computational complexity reduction, nonexponential failure distribution consideration, and repairable events in DFT is studied by a number of examples, and the results are then compared to those of the selected existing methods.