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Benefits of Bayesian Network Models by Christophe Simon, Philippe Weber

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4Dynamic Bayesian Networks: Integrating Environmental and Operating Constraints in Reliability Computation

4.1. Introduction

To take into account the uncertainty with the temporal aspect, system behavior is modeled by a random variable, which takes its values in finite states corresponding to the system states. The state space method is well known in dependability literature [COR 75, VIL 88, ANS 94, COC 97, AVE 99, GER 00] and also in industrial standards [IEC 06]. The models obtained estimate the failure probabilities of systems throughout their lifetime.

This method gives a graphical representation [VIL 88, p. 303; COC 97, p. 282] whose complexity depends on the hypotheses made that correspond to the real stochastic process. However, the complexity increases tremendously when the number of components increases. Indeed, the state space describing the system is built from the Cartesian product of the component states.

To reduce this problem, state aggregation techniques are proposed [COC 97, p. 282]. The Markov chains (MCs) obtained are usually compact. For instance, in [WEB 06, WEB 08, POU 09, WEB 12a] it was applied to wind turbine modeling and gives models with fewer states than the initial model. A new modeling approach has to satisfy such a compactness target.

Dynamic fault trees (DFTs) [DUG 92, MES 02] are one solution allowing us to describe a MC of great dimension. The DFT modeling is based on a graphical description language of the component combination (for instance, ...

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