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Sequential Interval Reliability for Discrete-Time Homogeneous Semi-Markov Repairable Systems

Author

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  • Vlad Stefan Barbu

    (Laboratory of Mathematics Raphaël Salem, University of Rouen-Normandy, UMR 6085, Avenue de l’Université, BP. 12, F76801 Saint-Étienne-du-Rouvray, France)

  • Guglielmo D’Amico

    (Department of Economics, University “G. d’Annunzio” of Chieti-Pescara, 66013 Pescara, Italy)

  • Thomas Gkelsinis

    (Laboratory of Mathematics Raphaël Salem, University of Rouen-Normandy, UMR 6085, Avenue de l’Université, BP. 12, F76801 Saint-Étienne-du-Rouvray, France)

Abstract

In this paper, a new reliability measure, named sequential interval reliability, is introduced for homogeneous semi-Markov repairable systems in discrete time. This measure is the probability that the system is working in a given sequence of non-overlapping time intervals. Many reliability measures are particular cases of this new reliability measure that we propose; this is the case for the interval reliability, the reliability function and the availability function. A recurrent-type formula is established for the calculation in the transient case and an asymptotic result determines its limiting behaviour. The results are illustrated by means of a numerical example which illustrates the possible application of the measure to real systems.

Suggested Citation

  • Vlad Stefan Barbu & Guglielmo D’Amico & Thomas Gkelsinis, 2021. "Sequential Interval Reliability for Discrete-Time Homogeneous Semi-Markov Repairable Systems," Mathematics, MDPI, vol. 9(16), pages 1-18, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:16:p:1997-:d:618629
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    References listed on IDEAS

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    1. Bulla, Jan & Bulla, Ingo, 2006. "Stylized facts of financial time series and hidden semi-Markov models," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2192-2209, December.
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    5. Bulla, Jan, 2006. "Application of Hidden Markov Models and Hidden Semi-Markov Models to Financial Time Series," MPRA Paper 7675, University Library of Munich, Germany.
    6. Guglielmo D’Amico & Raimondo Manca & Filippo Petroni & Dharmaraja Selvamuthu, 2021. "On the Computation of Some Interval Reliability Indicators for Semi-Markov Systems," Mathematics, MDPI, vol. 9(5), pages 1-23, March.
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    8. Guglielmo D’Amico & Jacques Janssen & Raimondo Manca, 2016. "Downward migration credit risk problem: a non-homogeneous backward semi-Markov reliability approach," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(3), pages 393-401, March.
    9. Guglielmo D’Amico & Jacques Janssen & Raimondo Manca, 2010. "Initial and Final Backward and Forward Discrete Time Non-homogeneous Semi-Markov Credit Risk Models," Methodology and Computing in Applied Probability, Springer, vol. 12(2), pages 215-225, June.
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    Citations

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    Cited by:

    1. Guglielmo D’Amico & Thomas Gkelsinis, 2024. "On a Mixed Transient–Asymptotic Result for the Sequential Interval Reliability for Semi-Markov Chains," Mathematics, MDPI, vol. 12(12), pages 1-18, June.
    2. D’Amico, Guglielmo & Petroni, Filippo, 2023. "ROCOF of higher order for semi-Markov processes," Applied Mathematics and Computation, Elsevier, vol. 441(C).
    3. P.-C.G. Vassiliou & Andreas C. Georgiou, 2021. "Markov and Semi-Markov Chains, Processes, Systems, and Emerging Related Fields," Mathematics, MDPI, vol. 9(19), pages 1-6, October.
    4. Ming-Na Tong & Fu-Qiang Shen & Chen-Xing Cui, 2022. "The Inverse Transformation of L-Hermite Model and Its Application in Structural Reliability Analysis," Mathematics, MDPI, vol. 10(22), pages 1-15, November.
    5. Fanping Wei & Jingjing Wang & Xiaobing Ma & Li Yang & Qingan Qiu, 2023. "An Optimal Opportunistic Maintenance Planning Integrating Discrete- and Continuous-State Information," Mathematics, MDPI, vol. 11(15), pages 1-19, July.

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