Parallel algorithm for finding modules of large-scale coherent fault trees

Abstract

The computation of the probability of the top event or minimal cut sets of fault trees is known as intractable NP-hard problems. Modularization can be used to reduce the computational cost of basic operations on fault trees efficiently. The idea of the linear time algorithm, as a very efficient and compact modules detecting algorithm, is visiting the nodes one by one with top-down depth-first left-most traversal of the tree. So the efficiency of the linear time algorithm is limited by nodes visiting time successively and serially, especially when confronting large-scale fault trees. Aiming at improving the efficiency of modularizing large-scale fault trees, this paper proposes a new parallel method to find all possible modules. Firstly, we transform the fault tree into a directed acyclic graph (DAG) and treat the terminal basic nodes as entries of the algorithm. And then, according to the proposed rules in this paper, we traverse the graph bottom-up from the terminal nodes and mark the internal nodes in a parallel way. Therefore, we can compare all internal nodes and decide which nodes are modules. Eventually, an experiment is carried out to compare the linear and parallel algorithm, and the result shows that the proposed parallel algorithm is efficient on handling large-scale fault trees.