Analytical Calculation and Rapid Simulation of Survival Signatures in Dynamic Fault Trees With Priority-AND Gates

Abstract

Many practical systems are often involved in sequence-dependent failure behaviors. The efficiency of analyzing these dynamic systems is limited by addressing sequential failure events (SFEs). The survival signature method has the potential to address this issue. However, the survival signature cannot be applied directly due to the existence of SFEs. In this article, the adapted survival signature-based methods are developed for the rapid analysis of dynamic systems modeled by dynamic fault trees with priority- <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">and</small> gates. First, we deduce the probabilistic expressions of SFEs under the survival signature paradigm using conditional probability. Second, an analytical method for accurately computing the survival signatures of dynamic systems is proposed. Third, for large-scale and highly coupled dynamic systems, a semianalytical method is proposed to obtain the survival signature through simulating the Boolean states of SFEs under given components’ state. Several numerical and practical engineering cases are examined to highlight the superiority of the proposed methods compared with the sequential binary decision diagram method and coarse Monte Carlo simulation.