Calculating exact top-event probabilities using Σ-Patrec
A. Sharif Heger, Jayaram K. Bhat, Desmond W. Stack, Dale V. Talbott · IEEE Transactions on Reliability · 1995
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 /spl Sigma/II algorithm of Corynen and the pattern recognition scheme of Keen et al. The PC-based program that is developed using this method is called /spl Sigma/II-Patrec and computes the exact probability of top-event of a system fault-tree model as defined by its cut sets. The /spl Sigma/II 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. /spl Sigma/II-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 /spl Sigma/II-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.