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

In: Stochastic Reliability and Maintenance Modeling

Author

Listed:
  • Julien Chiquet

    (Université d’Évry Val-d’Essonne)

  • Nikolaos Limnios

    (Université de Technologie de Compiègne)

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.

Suggested Citation

  • Julien Chiquet & Nikolaos Limnios, 2013. "Dynamical Systems with Semi-Markovian Perturbations and Their Use in Structural Reliability," Springer Series in Reliability Engineering, in: Tadashi Dohi & Toshio Nakagawa (ed.), Stochastic Reliability and Maintenance Modeling, edition 127, pages 191-218, Springer.
    • Handle: RePEc:spr:ssrchp:978-1-4471-4971-2_10
    DOI: 10.1007/978-1-4471-4971-2_10
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    Cited by:

    1. Blanke, D. & Bosq, D., 2016. "Detecting and estimating intensity of jumps for discretely observed ARMAD(1,1) processes," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 119-137.

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