A compositional semantics for Repairable Fault Trees with general distributions

TL;DR

This paper develops a compositional semantics for Repairable Fault Trees with general distributions, enabling accurate modeling and simulation of complex repair-dependent systems in risk assessment.

Contribution

It introduces a novel semantics based on Input/Output Stochastic Automata for RFTs, accommodating general distributions and supporting efficient simulation methods.

Findings

Semantics generates (weakly) deterministic models

Enables modeling with general continuous distributions

Supports rare event simulation with the FIG tool

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.