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A Semi-Markov Model with Geometric Renewal Processes

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Abstract

We consider a repairable system modeled by a semi-Markov process (SMP), where we include a geometric renewal process for system degradation upon repair, and replacement strategies for non-repairable failure or upon N repairs. First Pérez-Ocón and Torres-Castro studied this system (Pérez-Ocón and Torres-Castro in Appl Stoch Model Bus Ind 18(2):157–170, 2002) and proposed availability calculation using the Laplace Transform. In our work, we consider an extended state space for up and down times separately. This allows us to leverage the standard theory for SMP to obtain all reliability related measurements such as reliability, availability (point and steady-state), mean times and rate of occurrence of failures of the system with general initial law. We proceed with a convolution algebra, which allows us to obtain final closed form formulas for the above measurements. Finally, numerical examples are given to illustrate the methodology.

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Acknowledgements

Authors are grateful to both of referees for the comments to improve the presentation of this work.

Funding

**gqi Zhang is imbedded in the CSC-organization for their financial support.

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Author notes

  1. Mitra Fouladirad and Nikolaos Limnios contributed equally to this work.

Authors and Affiliations

  1. LIST3N, Université de Technologie de Troyes, 12 rue Marie Curie, Troyes, 10004, France

    **gqi Zhang

  2. Aix Marseille Université, M2P2, UMR CNRS 7340, Ecole Centrale Marseille, 38 Rue Frédéric Joliot Curie, Marseille, 13013, France

    **gqi Zhang & Mitra Fouladirad

  3. LMAC, Université de Technologie de Compiègne, 57 avenue de Landshut, Compiègne, 60200, France

    **gqi Zhang & Nikolaos Limnios

Authors
  1. **gqi Zhang
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  2. Mitra Fouladirad
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  3. Nikolaos Limnios
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All authors contribute to the work equally. All authors reviewed the manuscript.

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Correspondence to **gqi Zhang.

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Zhang, J., Fouladirad, M. & Limnios, N. A Semi-Markov Model with Geometric Renewal Processes. Methodol Comput Appl Probab 25, 85 (2023). https://doi.org/10.1007/s11009-023-10060-z

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  • DOI: https://doi.org/10.1007/s11009-023-10060-z

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