Uncertainty Handling in Quantitative BDD-Based Fault-Tree Analysis by Interval Computation

In fault-tree analysis, probabilities of failure of components are often assumed to be precise. However this assumption is seldom verified in practice. There is a large literature on the computation of the probability of the top (dreadful) event of the fault-tree, based on the representation of logical formulas in the form of binary decision diagrams (BDD). When probabilities of atomic propositions are ill-known and modelled by intervals, BDD-based algorithms no longer apply to the computation of the top probability interval. This paper investigates this question for general Boolean expressions, and proposes an approach based on interval methods, relying on the analysis of the structure of the Boolean formula. The considered application deals with the fault-tree-based analysis of the reliability of aircraft operations.