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M out of n inspected systems subject to shocks in random environment

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  • Kenzin, Moshe
  • Frostig, Esther

Abstract

Consider a parallel redundant system, consisting n components, that is subject to shocks. The shocks cause the components to fail with certain probabilities. Shocks arrival rate and components’ failure probabilities may depend on an external Markovian environment. We consider warm and cold stand-by systems. Systems’ failures are silent. The system is maintained through inspection and repair/replacement. We propose several state-dependent maintenance policies and derive system availability and cost function.

Suggested Citation

  • Kenzin, Moshe & Frostig, Esther, 2009. "M out of n inspected systems subject to shocks in random environment," Reliability Engineering and System Safety, Elsevier, vol. 94(8), pages 1322-1330.
    • Handle: RePEc:eee:reensy:v:94:y:2009:i:8:p:1322-1330
    DOI: 10.1016/j.ress.2009.02.005
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    References listed on IDEAS

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    1. Zhao, Jianmin & Chan, A.H.C. & Roberts, C. & Madelin, K.B., 2007. "Reliability evaluation and optimisation of imperfect inspections for a component with multi-defects," Reliability Engineering and System Safety, Elsevier, vol. 92(1), pages 65-73.
    2. Chelbi, Anis & Ait-Kadi, Daoud, 2000. "Generalized inspection strategy for randomly failing systems subjected to random shocks," International Journal of Production Economics, Elsevier, vol. 64(1-3), pages 379-384, March.
    3. Sarkar, Jyotirmoy & Sarkar, Sahadeb, 2001. "Availability of a periodically inspected system supported by a spare unit, under perfect repair or perfect upgrade," Statistics & Probability Letters, Elsevier, vol. 53(2), pages 207-217, June.
    4. Courtois, Pierre-Jacques & Delsarte, Philippe, 2006. "On the optimal scheduling of periodic tests and maintenance for reliable redundant components," Reliability Engineering and System Safety, Elsevier, vol. 91(1), pages 66-72.
    5. Toshio Nakagawa, 2005. "Maintenance Theory of Reliability," Springer Series in Reliability Engineering, Springer, number 978-1-84628-221-8, February.
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    Cited by:

    1. Hazra, Nil Kamal & Finkelstein, Maxim & Cha, Ji Hwan, 2022. "On a hazard (failure) rate process with delays after shocks," Statistics & Probability Letters, Elsevier, vol. 181(C).
    2. Ji Hwan Cha & Massimiliano Giorgio, 2018. "Modelling of Marginally Regular Bivariate Counting Process and its Application to Shock Model," Methodology and Computing in Applied Probability, Springer, vol. 20(4), pages 1137-1154, December.
    3. Cha, Ji Hwan & Finkelstein, Maxim & Levitin, Gregory, 2018. "Optimal mission abort policy for partially repairable heterogeneous systems," European Journal of Operational Research, Elsevier, vol. 271(3), pages 818-825.
    4. Ji Hwan Cha & Maxim Finkelstein, 2018. "On a New Shot Noise Process and the Induced Survival Model," Methodology and Computing in Applied Probability, Springer, vol. 20(3), pages 897-917, September.
    5. Ji Hwan Cha & Maxim Finkelstein, 2019. "On some characteristics of quality for systems operating in a random environment," Journal of Risk and Reliability, , vol. 233(2), pages 257-267, April.
    6. Montoro-Cazorla, Delia & Pérez-Ocón, Rafael, 2015. "A shock and wear model with dependence between the interarrival failures," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 339-352.
    7. Maxim Finkelstein & Gregory Levitin, 2018. "Optimal Mission Duration for Partially Repairable Systems Operating in a Random Environment," Methodology and Computing in Applied Probability, Springer, vol. 20(2), pages 505-516, June.
    8. Maxim Finkelstein & Gregory Levitin, 2020. "On missions’ quality of performance for systems with partially or completely observable degradation," Journal of Risk and Reliability, , vol. 234(5), pages 676-685, October.
    9. Maxim Finkelstein & Gregory Levitin, 2018. "Optimal mission duration for systems subject to shocks and internal failures," Journal of Risk and Reliability, , vol. 232(1), pages 82-91, February.
    10. Levitin, Gregory & Finkelstein, Maxim & Dai, Yuanshun, 2018. "Optimizing availability of heterogeneous standby systems exposed to shocks," Reliability Engineering and System Safety, Elsevier, vol. 170(C), pages 137-145.
    11. Montoro-Cazorla, Delia & Pérez-Ocón, Rafael, 2014. "A reliability system under different types of shock governed by a Markovian arrival process and maintenance policy K," European Journal of Operational Research, Elsevier, vol. 235(3), pages 636-642.
    12. Cha, Ji Hwan & Finkelstein, Maxim, 2016. "On some properties of shock processes in a ‘natural’ scale," Reliability Engineering and System Safety, Elsevier, vol. 145(C), pages 104-110.
    13. Montoro-Cazorla, Delia & Pérez-Ocón, Rafael, 2011. "Two shock and wear systems under repair standing a finite number of shocks," European Journal of Operational Research, Elsevier, vol. 214(2), pages 298-307, October.
    14. Cha, Ji Hwan & Finkelstein, Maxim, 2016. "New shock models based on the generalized Polya process," European Journal of Operational Research, Elsevier, vol. 251(1), pages 135-141.

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