A Computational Framework for Prioritization of Events in Fault Tree Analysis Under Interval-Valued Probabilities

Abstract

In probabilistic safety assessment (PSA), the assessed events can be prioritized using risk importance measures, which are functions of the events' failure probabilities. These probabilities can be uncertain, and consequently the resulting prioritization can be uncertain too. In this paper, we present a framework for computing the impacts of this uncertainty, which is modeled by interval-valued probabilities that establish lower and upper bounds, within which the probability may vary. Specifically, we make pairwise comparisons between events so that an event is said to dominate another if its risk importance measure is at least as high for all event probabilities that are within their respective intervals, and strictly higher for some probabilities. The dominance relations establish a partial order which can be visualized as a directed acyclic graph. We illustrate our method by analyzing the fault tree that represents the residual heat removal system of a nuclear reactor. The results for this fault tree with 31 events and 147 minimal cut sets was solved in seconds using a tailored algorithm. Theoretical properties of the algorithm suggest that much larger models can still be solved in reasonable time.