Calculating exact top-event probabilities using Σ-Patrec

This paper presents a method for calculating top-event exact probability. This responds to a surge in the application of probabilistic risk assessment (PRA) techniques to ecological and weapon safety assessments. In these domains, basic event probabilities can be large; events characterizing human error and some natural phenomena are typical examples. The method described combines the ΣII algorithm of Corynen and the pattern recognition scheme of Keen et al. The PC-based program that is developed using this method is called ΣII-Patrec and computes the exact probability of top-event of a system fault-tree model as defined by its cut sets. The ΣII module partitions and disjoints the cut sets and solves the resultant sub-models recursively. The pattern recognition module reduces the computational complexity by recognizing repeated sub-models in the calculation process and thus avoiding repeated evaluations. ΣII-Patrec is designed to quantify the fault-tree models of both coherent and incoherent systems, and interfaces with the graphic package, SEATREE, for interactive generation of fault trees. In the anticipated case, the ΣII-Patrec method of evaluation of exact top-event probability is polynomial in the number of cut sets; it can, however, be weakly exponential in the worst case. Either way, this method results in a substantial reduction in computation requirements compared to the inclusion-exclusion method. The algorithm is described through an example problem. The results of several experiments with large accident sequence are also presented