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Dynamical Systems with Semi-Markovian Perturbations and Their Use in Structural Reliability

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Stochastic Reliability and Maintenance Modeling

Part of the book series: Springer Series in Reliability Engineering ((RELIABILITY,volume 9))

Abstract

The aim of this chapter is to present dynamical systems evolving in continuous-time and perturbed by semi-Markov processes (SMP). We investigate both probabilistic modeling and statistical estimation of such models. This work was initially developed in order to study cracking problems for the confinement device in nuclear power plants, where a jump Markov process was used as the perturbing process. The new key element here is the use of SMPs instead of Markov ones for the randomization of the system. Several numerical illustrations in reliability are investigated, accompanied with guidelines for a practical numerical implementation.

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Acknowledgments

This chapter is dedicated to Professor Shunji Osaki for his 70th Birthday. It deals with semi-Markov processes and reliability which is the main area of expertise of Prof. Osaki. He has done many contributions to this field, a lot of them being included in his book “Stochastic System Reliability Modeling” (see Ref. [21] below), which is used as a basic reference by many researchers by the world including the present authors.

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Authors and Affiliations

  1. UMR CNRS 8071–USC INRA, Université d’Évry Val-d’Essonne, Évry, France

    Julien Chiquet

  2. Université de Technologie de Compiègne, Compiègne, France

    Nikolaos Limnios

Authors
  1. Julien Chiquet
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  2. Nikolaos Limnios
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Corresponding author

Correspondence to Julien Chiquet .

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Editors and Affiliations

  1. , Department of Information Engineering, Hiroshima University, Kagamiyama 1-4-1, Higashi-Hiroshima, 739-8527, Japan

    Tadashi Dohi

  2. , Dept. of Business administration, Aichi Institute of Technology, Yachigusa, Yagusa-cho 1247, Toyota, 470-0392, Japan

    Toshio Nakagawa

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Chiquet, J., Limnios, N. (2013). Dynamical Systems with Semi-Markovian Perturbations and Their Use in Structural Reliability. In: Dohi, T., Nakagawa, T. (eds) Stochastic Reliability and Maintenance Modeling. Springer Series in Reliability Engineering, vol 9. Springer, London. https://doi.org/10.1007/978-1-4471-4971-2_10

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  • DOI: https://doi.org/10.1007/978-1-4471-4971-2_10

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  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-4970-5

  • Online ISBN: 978-1-4471-4971-2

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