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Évaluation de la fiabilité des systèmes modélisés par arbres de défaillances grâce aux techniques de satisfiabilité

Margaux Duroeulx 1, 2, 3
1 MOSEL - Proof-oriented development of computer-based systems
LORIA - FM - Department of Formal Methods
2 VERIDIS - Modeling and Verification of Distributed Algorithms and Systems
MPII - Max-Planck-Institut für Informatik, Inria Nancy - Grand Est, LORIA - FM - Department of Formal Methods
Abstract : This thesis focuses on designing critical systems, those functioning is impacted by failures that could be dangerous for goods and people. During its design, it is crucial to convey a dependability analysis in order to determine the potential failures, their criticity and their probability of occurrence. The aim of this thesis is to involve satisfiability techniques in the computation of the reliability of the system: its probability to ensure its mission for a given time. In the first part, we consider static systems, those for which the functioning only depends on the functioning of their components functioning. We model the system by a fault tree, which is a widespread modeling tool in the reliability community, from which we can obtain the structure function. The structure function is a formula describing the combinations of components failure which are tolerated or not by the system. We also model the system by a Hasse diagram, which represents the states of the system depending on the states of the components. The probabilistic assessment of the trust placed to the system is based on the reliability function determined from the Hasse diagram. In the second part, we consider dynamic systems, for which the order between failures has an impact on the system. For example, it is the case for electric generators, which deprive the other components of electricity when they fail. In order to adapt to dynamic systems, the approach developed of the first part, we define minimal tie set sequences as the extension of minimal tie sets for dynamic systems, and we compute them by using satisfiability techniques. We also propose an adaptation of Hasse diagrams for dynamic systems to determine the reliability function.
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Margaux Duroeulx. Évaluation de la fiabilité des systèmes modélisés par arbres de défaillances grâce aux techniques de satisfiabilité. Performance et fiabilité [cs.PF]. Université de Lorraine, 2020. Français. ⟨NNT : 2020LORR0026⟩. ⟨tel-02881242⟩

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