Dynamic Bayesian Networks for modeling advanced Fault Tree features in dependability analysis

Fault Trees (FT) are one of the most popular techniques for dependability analysis of large, safety critical systems. They allow one to represent the combination of elementary causes that lead to the occurrence of an undesired catastrophic event named the Top Event (TE). By specifying failure probabilities on the basic components of the modeled system (the elementary causes of the TE, also called basic events), then the whole system unreliability (probability of the TE) at a given mission time can be computed. In recent years, an effort has been documented in the literature, aimed at increasing the modeling power of FT by including new primitive gates, able to accommodate complex kinds dependencies. This augmented FT language is referred to by the authors as dynamic FT (Dugan 1992, Dugan 1993, Manian 1999). Dynamic Fault Trees (DFT) introduce four basic (dynamic) gates: the warm spare (WSP), the sequence enforcing (SEQ), the probabilistic dependency (PDEP) and the priority AND (PAND). WSP are dynamic gates modeling one or more principal components that can be substituted by one or more backups (spares), with the same functionality (figure 1(a)). The WSP gate fails when the number of operational powered spares and/or principal components is less than the minimum required. In particular spares can fail even while they are dormant, but the failure rate of an unpowered spare is lower than the failure rate of the corresponding powered one. More precisely, being λ the failure rate of a powered spare, the failure rate of the unpowered spare is αλ, with 0<=α<=1 called the dormancy factor. Spares are more properly called “hot” if α=1 and “cold” if α=0. ABSTRACT: Fault Trees (FT) are one of the most popular techniques for dependability analysis of large, safety critical systems. It has been shown (Bobbio 2001) that FT can be directly mapped into Bayesian Networks (BN) and that the basic inference techniques on the latter may be used to obtain classical parameters computed from the former. In this paper, we show how BN can provide a unified framework in which also Dynamic FT (DFT), a recent extensions able to treat complex types of dependencies, can be represented. In particular, we propose to characterize dynamic gates within the Dynamic Bayesian Network framework (DBN), by translating all the basic dynamic gates into the corresponding DBN model. The approach has been tested on a complex example taken from the literature. Our experimental results testify how DBN can be safely resorted to if a quantitative analysis of the system is required. Moreover, they are able to enhance both the modeling and the analysis capabilities of classical FT approaches, by representing more general dependencies and by performing general inference on the resulting model.