Complete Sequence Generation Algorithm for Reliability Analysis of Dynamic Systems with Sequence-Dependent Failures

Sequence-dependent failures can be found in many real-life fault-tolerant systems where the occurrence order of fault events is important. The priority-AND (pAND) gates have been used to model such dependent behavior in the dynamic fault tree (DFT) reliability analysis. In order to overcome limitations of existing approaches (e.g., state-space-based or simulation-based methodologies), a combinatorial and analytical method has recently been proposed, which offers an exact and efficient solution to the reliability analysis of dynamic systems with sequence-dependent failures. Using this approach, it is necessary to adopt an efficient algorithm to enumerate the list of complete sequences from partial sequences. Thus in this paper, we propose a sorting algorithm for enumerating complete sequences. of events from the partial orders/sequences of the events for the reliability analysis of systems subject to sequence-dependent failure behavior. The generation algorithm is based on the topological sorting algorithm which finds the optimal sequence that satisfies the precedence constraints in a directed acyclic graph. Several examples are given to illustrate the basics and application of the proposed approach.