Rapid computation of survival signature for dynamic fault tree based on sequential binary decision diagram and multidimensional array

Many practical safety-critical systems typically exhibit sequence-dependent failure behaviors, limiting the efficiency of analyzing these systems. Although the survival signature-based method can address this problem to a certain extent, the dependence on Boolean states constrains its application to large systems. In this study, we present a novel method that leverages the sequential binary decision diagram (SBDD) and multidimensional array to rapidly compute survival signatures for dynamic fault trees (DFTs) of these systems. These dynamic nodes in the SBDD are represented through multidimensional arrays, which are then utilized as inputs for the subsequent computations. Ultimately, survival signatures are obtained by iteratively computing the multidimensional arrays. Additionally, two practical engineering cases are examined to highlight the superiority of the proposed methods over other methods. Compared with Boolean state vector-based methods, the proposed method achieves a 689-fold and 209-fold increase in efficiency for calculating survival signatures in their respective cases. Compared with the Monte Carlo (MC) simulation, the simulation efficiency for the reliability results improve by 60-fold and 201-fold in their respective cases.