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On the Computation of Some Interval Reliability Indicators for Semi-Markov Systems

Author

Listed:
  • Guglielmo D’Amico

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

  • Raimondo Manca

    (MEMOTEF Department, University of Rome, “La Sapienza”, 00185 Rome, Italy)

  • Filippo Petroni

    (Department of Management, Marche Polytechnic University, 60121 Ancona, Italy)

  • Dharmaraja Selvamuthu

    (Department of Mathematics, Indian Institute of Technology Delhi, New Delhi 110016, India)

Abstract

In this paper, we computed general interval indicators of availability and reliability for systems modelled by time non-homogeneous semi-Markov chains. First, we considered duration-dependent extensions of the Interval Reliability and then, we determined an explicit formula for the availability with a given window and containing a given point. To make the computation of the window availability, an explicit formula was derived involving duration-dependent transition probabilities and the interval reliability function. Both interval reliability and availability functions were evaluated considering the local behavior of the system through the recurrence time processes. The results are illustrated through a numerical example. They show that the considered indicators can describe the duration effects and the age of the multi-state system and be useful in real-life problems.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:5:p:575-:d:512649
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    References listed on IDEAS

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    1. Moura, Márcio das Chagas & Droguett, Enrique López, 2009. "Mathematical formulation and numerical treatment based on transition frequency densities and quadrature methods for non-homogeneous semi-Markov processes," Reliability Engineering and System Safety, Elsevier, vol. 94(2), pages 342-349.
    2. D׳Amico, Guglielmo & Petroni, Filippo & Prattico, Flavio, 2015. "Reliability measures for indexed semi-Markov chains applied to wind energy production," Reliability Engineering and System Safety, Elsevier, vol. 144(C), pages 170-177.
    3. Jacques Janssen & Raimondo Manca, 2001. "Numerical Solution of non-Homogeneous Semi-Markov Processes in Transient Case," Methodology and Computing in Applied Probability, Springer, vol. 3(3), pages 271-293, September.
    4. Cui, Lirong & Chen, Jianhui & Wu, Bei, 2017. "New interval availability indexes for Markov repairable systems," Reliability Engineering and System Safety, Elsevier, vol. 168(C), pages 12-17.
    5. Yi, He & Cui, Lirong & Shen, Jingyuan & Li, Yan, 2018. "Stochastic properties and reliability measures of discrete-time semi-Markovian systems," Reliability Engineering and System Safety, Elsevier, vol. 176(C), pages 162-173.
    6. Yunhui Hou & Nikolaos Limnios & Walter Schön, 2017. "On the Existence and Uniqueness of Solution of MRE and Applications," Methodology and Computing in Applied Probability, Springer, vol. 19(4), pages 1241-1250, December.
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    Cited by:

    1. 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.
    2. 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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