Differential, criticality and Birnbaum importance measures: An application to basic event, groups and SSCs in event trees and binary decision diagrams

Recent works [Epstein S, Rauzy A. Can we trust PRA? Reliab Eng Syst Safety 2005; 88:195–205] have questioned the validity of traditional fault tree/event tree (FTET) representation of probabilistic risk assessment problems. In spite of whether the risk model is solved through FTET or binary decision diagrams (BDDs), importance measures need to be calculated to provide risk managers with information on the risk/safety significance of system structures and components (SSCs). In this work, we discuss the computation of the Fussel–Vesely (FV), criticality, Birnbaum, risk achievement worth (RAW) and differential importance measure (DIM) for individual basic events, basic event groups and components. For individual basic events, we show that these importance measures are linked by simple relations and that this enables to compute basic event DIMs both for FTET and BDD codes without additional model runs. We then investigate whether/how importance measures can be extended to basic event groups and components. Findings show that the estimation of a group Birnbaum or criticality importance is not possible. On the other hand, we show that the DIM of a group or of a component is exactly equal to the sum of the DIMs of the corresponding basic events and can therefore be found with no additional model runs. The above findings hold for both the FTET and the BDD methods.