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A Semi-Markov Model with Geometric Renewal Processes

Author

Listed:
  • Jingqi Zhang

    (Université de Technologie de Troyes
    Ecole Centrale Marseille
    Université de Technologie de Compiègne)

  • Mitra Fouladirad

    (Ecole Centrale Marseille)

  • Nikolaos Limnios

    (Université de Technologie de Compiègne)

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.

Suggested Citation

  • Jingqi Zhang & Mitra Fouladirad & Nikolaos Limnios, 2023. "A Semi-Markov Model with Geometric Renewal Processes," Methodology and Computing in Applied Probability, Springer, vol. 25(4), pages 1-20, December.
    • Handle: RePEc:spr:metcap:v:25:y:2023:i:4:d:10.1007_s11009-023-10060-z
    DOI: 10.1007/s11009-023-10060-z
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    References listed on IDEAS

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    1. Ouhbi, Brahim & Limnios, Nikolaos, 2002. "The rate of occurrence of failures for semi-Markov processes and estimation," Statistics & Probability Letters, Elsevier, vol. 59(3), pages 245-255, October.
    2. Arnold, Richard & Chukova, Stefanka & Hayakawa, Yu & Marshall, Sarah, 2020. "Geometric-Like Processes: An Overview and Some Reliability Applications," Reliability Engineering and System Safety, Elsevier, vol. 201(C).
    3. Wu, Bei & Cui, Lirong & Fang, Chen, 2019. "Reliability analysis of semi-Markov systems with restriction on transition times," Reliability Engineering and System Safety, Elsevier, vol. 190(C), pages 1-1.
    4. Bei Wu & Brenda Ivette Garcia Maya & Nikolaos Limnios, 2021. "Using Semi-Markov Chains to Solve Semi-Markov Processes," Methodology and Computing in Applied Probability, Springer, vol. 23(4), pages 1419-1431, December.
    5. Nikolaos Limnios, 2012. "Reliability Measures of Semi-Markov Systems with General State Space," Methodology and Computing in Applied Probability, Springer, vol. 14(4), pages 895-917, December.
    Full references (including those not matched with items on IDEAS)

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