A compositional semantics for Repairable Fault Trees with general distributions

Abstract

Fault Tree Analysis (FTA) is a prominent technique in industrial and scientific risk assessment. Repairable Fault Trees (RFT) enhance the classical Fault Tree (FT) model by introducing the possibility to describe complex dependent repairs of system components. Usual frameworks for analyzing FTs such as BDD, SBDD, and Markov chains fail to assess the desired properties over RFT complex models, either because these become too large, or due to cyclic behaviour introduced by dependent repairs. Simulation is another way to carry out this kind of analysis. In this paper we review the RFT model with Repair Boxes as introduced by Daniele Codetta-Raiteri. We present compositional semantics for this model in terms of Input/Output Stochastic Automata, which allows for the modelling of events occurring according to general continuous distribution. Moreover, we prove that the semantics generates (weakly) deterministic models, hence suitable for discrete event simulation, and prominently for rare event simulation using the FIG tool.

Efficient and Generic Algorithms for Quantitative Attack Tree Analysis

“…Instead, in this work we follow [26,27] and call an AT dynamic when its structure includes a sequential-AND gate-so its semantics must distinguish among different execution orders of the basic attack steps. This is akin to the notions used in fault tree analysis, where dynamic gates like priority-AND in dynamic fault trees have similar semantics to sequential-AND in ATs [28,57].…”

Automated Rare Event Simulation for Fault Tree Analysis via Minimal Cut Sets

“…The mathematical definition of a compositional semantics for repairable dfts that allows this approach is introduced in [20]; moreover, [3] formally defines simulation traces in such iosa semantics.…”

“…Note however that repairs do not affect mcs. Thus, in this work we consider the class of repairable fault trees (rft) described in [20]-but excluding PAND gates.…”

“…Thus, SPARE gates are essentially ANDs. Moreover, FDEPs in rfts are non-destructive: if a failed trigger is repaired, the BEs affected by the gate become available (not necessarily operational) once again [20]. This can be modelled with OR gates: in Fig.…”

“…The theory described in this section is piggybacked in the tool chain of [3], where rfts are input in an extended version of the Galileo textual format [26,27]. A Java converter builds its iosa semantics following [20], as well as the compositional importance function of [3]. Model and function are then fed to the tool, which implements various flavours of (importance splitting) res.…”