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International Conference on Quantitative Evaluation of Systems

QEST 2015: Quantitative Evaluation of Systems pp 176–191Cite as

A Numerical Analysis of Dynamic Fault Trees Based on Stochastic Bounds

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9259))

Abstract

We present a numerical method based on stochastic bounds and computations of discrete distributions to get the transient reliability of a system described by a Dynamic Fault Tree. We show that the gates of the tree are associated to simple operators on the probability distributions of the time to failure. We also prove that almost all operators are stochastically monotone, which allows us to simplify the computation complexity using stochastic bounds. We show that replicated events and functional dependency gates can be analyzed with conditional probabilities which can be handled with the same techniques but with a higher complexity. Finally we show the tradeoff between the precision of the approach and the complexity of the computations.

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Acknowledgements

The authors are supported by grant ANR-12-MONU-00019.

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Authors and Affiliations

  1. PRiSM, CNRS and University Versailles St Quentin, Versailles, France

    J. M. Fourneau

  2. LACL, UPEC, Créteil, France

    Nihal Pekergin

Authors
  1. J. M. Fourneau
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  2. Nihal Pekergin
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Corresponding author

Correspondence to J. M. Fourneau .

Editor information

Editors and Affiliations

  1. Universidad de Zaragoza, Zaragoza, Spain

    Javier Campos

  2. University of Twente, Enschede, The Netherlands

    Boudewijn R. Haverkort

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Fourneau, J.M., Pekergin, N. (2015). A Numerical Analysis of Dynamic Fault Trees Based on Stochastic Bounds. In: Campos, J., Haverkort, B. (eds) Quantitative Evaluation of Systems. QEST 2015. Lecture Notes in Computer Science(), vol 9259. Springer, Cham. https://doi.org/10.1007/978-3-319-22264-6_12

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  • DOI: https://doi.org/10.1007/978-3-319-22264-6_12

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-22263-9

  • Online ISBN: 978-3-319-22264-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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