Algebraic modelling of Dynamic Fault Trees, contribution to qualitative and quantitative analysis

Abstract

In the context of the reliability of critical systems, we focus on Dynamic Fault Tree (DFT) analysis. Our contribution is the definition of an algebraic framework allowing to determine the structure function of DFTs and to extend the analytical methods commonly used to analyze Static Fault Trees to DFTs. First, we review the main approaches which allow to analyze DFTs, as well as their limits. Then, the algebraic framework allowing the modelling of DFTs is presented. This algebraic framework is based on a temporal model of events, and on the definition of three temporal operators allowing to model the sequences of appearance of events. These temporal operators allow to algebraically define the behaviour of dynamic gates, and hence the structure function of DFTs. A probabilistic model of these dynamic gates is given to determine the failure probability of the top event of DFTs from this structure function. Finally, we show how the structure function of DFTs can be simplified to a canonical form thanks to some theorems and to a minimal form thanks to the definition of a minimization criterion. Last, we show how DFTs can be analyzed analytically and directly from this minimal canonical form of the structure function. We illustrate this approach on two DFT examples from the literature.

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