A stochastic analysis of competing failures with propagation effects in functional dependency gates

Various dynamic gates have been utilized to model behaviors in dynamic fault trees (DFTs). For the functional dependency relationship among different components, a functional dependency (FDEP) gate models the scenario that the failure of some trigger events may result in the failures of other components. Conventionally, dependent relationships are modeled by an OR gate for systems with a perfect fault coverage. However, this is usually inaccurate, due to the effect of different types of failures, including local and propagated failures. A propagated failure originating from a component may affect the status of other dependent components. However, whether this occurs or not is determined by the failure order of the trigger and dependent events. A conventional DFT analysis incurs a high computational complexity for this scenario. In this article, a stochastic analysis is performed for an FDEP gate under imperfect fault coverage. The reliability of a system with competing failures can be efficiently predicted by the proposed stochastic analysis. Furthermore, the encoding using the non-Bernoulli sequence with random permutation of fixed number of ones and zeros enables an effective modeling of any time-to-failure distribution for the components. The corresponding efficiency and accuracy are revealed by the analysis of several benchmarks.