An Algorithm for Exact Fault-Tree Probabilities without Cut Sets

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Abstract
The algorithm presented in this paper, TDPP, is a top-down recursive algorithm to evaluate fault-tree probabilities. Unlike most existing methodologies, TDPP does not use cut sets, and it evaluates exact probabilities rather than approximations. Implemented in Pascal on a microcomputer, TDPP is sometimes competitive with truncation methodologies commonly used on mainframes. Even in the case of noncoherent fault trees with replicated inputs, there are conceptually simple uses of recursion to evaluate fault-tree probabilities. Although in larger trees elementary approaches usually perform poorly, their pedagogical value is appreciable. Some simpler recursive algorithms are used as an introduction to TDPP. The algorithm TDPP is very well suited to microcomputer use. While collection of cut sets may be memory intensive, probability evaluation is not. For those who want to free themselves from mainframes and canned software that may not be readily available, the TDPP algorithm offers an alternative. There is no need, on moderate sized problems, to settle for approximations or bounds on probabilities. Examples taken from the literature are used to show that TDPP applies to noncoherent fault trees of 50-100 nodes. While cut sets are useful in their own right in determining the relative importance of events, TDPP demonstrates that serious efforts to find fault-tree probabilities do not necessarily depend on a prior determination of cut sets.

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