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Uncertainty Analysis in Fault Tree Models with Dependent Basic Events

Authors

  • Nicola Pedroni,

    1. Energy Department, Politecnico di Milano, Via Ponzio, Milano, Italy
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  • Enrico Zio

    Corresponding author
    1. Chair of system science and the energetic challenge, Electricitè de France-Ecole Centrale de Paris and Supelec, Chatenay Malabry-Cedex, France
    • Energy Department, Politecnico di Milano, Via Ponzio, Milano, Italy
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Address correspondence to Enrico Zio, Electricitè de France-Ecole Centrale de Paris and Supelec, Grande Voie des Vignes, 92295, Chatenay Malabry-Cedex, France; tel: +33-01-41-13-16-06; fax: +33-01-41-13-12-72; enrico.zio@ecp.fr; enrico.zio@supelec.fr.

Abstract

In general, two types of dependence need to be considered when estimating the probability of the top event (TE) of a fault tree (FT): “objective” dependence between the (random) occurrences of different basic events (BEs) in the FT and “state-of-knowledge” (epistemic) dependence between estimates of the epistemically uncertain probabilities of some BEs of the FT model. In this article, we study the effects on the TE probability of objective and epistemic dependences. The well-known Frèchet bounds and the distribution envelope determination (DEnv) method are used to model all kinds of (possibly unknown) objective and epistemic dependences, respectively. For exemplification, the analyses are carried out on a FT with six BEs. Results show that both types of dependence significantly affect the TE probability; however, the effects of epistemic dependence are likely to be overwhelmed by those of objective dependence (if present).

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