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

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-and 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.

I. Introduction

Safety-critical systems have become a cornerstone of modern society. Many safety-critical systems are often involved in sequence-dependent failure behaviors due to complex redundancy design and management (e.g., aerospace systems, chemical process systems, and nuclear power plants). The failure of these dynamic systems depends not only on combinations of components but also the failure sequences of the components, and they typically play a key role in ensuring the safety of the whole system. Thus, it is very significant to precisely evaluate the reliability of these dynamic systems. The traditional static fault tree is a widely used method for performing reliability evaluations of various large-scale safety-critical systems due to its advantages of intuitiveness and ability to integrate analysis techniques [1], [2]. However, it cannot take into account sequential failure behaviors. In fact, it is not entirely reasonable for such safety-critical systems to simply regard a system failure as a combination of some component failures. To capture these sequential failure behaviors, DFTs [3], [4], [5] have been developed.