A Truncation Methodology for Evaluating Large Fault Trees

Probabilistic risk assessment (PRA) of a nuclear power plant often involves evaluating large fault trees (eg, trees with more than 1000 basic events and 1000 gates). It is desired to generate the dominant minimal cut sets (MCSs) in order to gain engineering insight, to estimate the top event probability, and to calculate the frequency of reactor core damage. To estimate the top event probability with computers, the usual practice has been to neglect those MCSs of the fault tree that have a probability of less than some cut-off value; the cut-off value is subjectively selected by the analyst. This method of truncation eliminates some MCSs, and thus simplifies the fault tree but does not help the analyst to estimate the truncation error. This source of uncertainty has been a concern in PRA calculations. A better method of truncation, based on both cut-set size and cut-set probability [Combined Truncation (CT) methodology] is developed and discussed in this paper. With this method, the analyst is able to estimate the maximum error that can occur in the truncation process. In the CT methodology the analyst estimates a parameter which is a function of the number of primary events in the fault tree, and the highest probability associated with the basic events in the fault tree. From that parameter value, the analyst then determines the level of truncation necessary and the associated maximum error of truncation.