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Modeling the evolution of system reliability performance under alternative environments

Author

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  • Alan Hawkes
  • Lirong Cui
  • Zhihua Zheng

Abstract

The dynamics of a system represented by a finite-state Markov process operating under two alternating regimes, for example, day/night, machine working/machine idling, etc., are modeled in this article. The transition rate matrices under the two regimes will usually be different. Also, the set of states of the system that are regarded as satisfactory may depend on the regime in operation: for example, a particular state of the system that may be regarded as satisfactory by day might not be tolerated at night (e.g., the headlights on a car not working). It is assumed that the regime durations are random variables and results are obtained for the availability of such a system and probability distributions for uptimes. Results and numerical examples are also given for two special cases: (i) when the regimes are of fixed duration; and (ii) when the regime durations have negative exponential distributions.

Suggested Citation

  • Alan Hawkes & Lirong Cui & Zhihua Zheng, 2011. "Modeling the evolution of system reliability performance under alternative environments," IISE Transactions, Taylor & Francis Journals, vol. 43(11), pages 761-772.
    • Handle: RePEc:taf:uiiexx:v:43:y:2011:i:11:p:761-772
    DOI: 10.1080/0740817X.2010.551758
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    Citations

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    Cited by:

    1. Jingyuan Shen & Lirong Cui, 2017. "Reliability performance for dynamic multi-state repairable systems with regimes," IISE Transactions, Taylor & Francis Journals, vol. 49(9), pages 911-926, September.
    2. Shijia Du & Lirong Cui & Cong Lin, 2016. "Some reliability indexes and sojourn time distributions for a repairable degradation model," Journal of Risk and Reliability, , vol. 230(3), pages 334-349, June.
    3. He Yi & Lirong Cui & Narayanaswamy Balakrishnan, 2022. "On the Derivative Counting Processes of First- and Second-order Aggregated Semi-Markov Systems," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1849-1875, September.
    4. Cui, Lirong & Wu, Bei, 2019. "Extended Phase-type models for multistate competing risk systems," Reliability Engineering and System Safety, Elsevier, vol. 181(C), pages 1-16.
    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. Zhengxin Zhang & Xiaosheng Si & Changhua Hu & Xiangyu Kong, 2015. "Degradation modeling–based remaining useful life estimation: A review on approaches for systems with heterogeneity," Journal of Risk and Reliability, , vol. 229(4), pages 343-355, August.
    7. Wu, Bei & Zhang, Yamei & Zhao, Songzheng, 2023. "Modeling coupled effects of dynamic environments and zoned shocks on systems under dependent failure processes," Reliability Engineering and System Safety, Elsevier, vol. 231(C).
    8. Du, Shijia & Zeng, Zhiguo & Cui, Lirong & Kang, Rui, 2017. "Reliability analysis of Markov history-dependent repairable systems with neglected failures," Reliability Engineering and System Safety, Elsevier, vol. 159(C), pages 134-142.
    9. Yi, He & Cui, Lirong, 2017. "Distribution and availability for aggregated second-order semi-Markov ternary system with working time omission," Reliability Engineering and System Safety, Elsevier, vol. 166(C), pages 50-60.
    10. 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.
    11. Jingyuan Shen & Alaa Elwany & Lirong Cui, 2018. "Reliability modeling for systems degrading in K cyclical regimes based on gamma processes," Journal of Risk and Reliability, , vol. 232(6), pages 754-765, December.
    12. Shen, Jingyuan & Cui, Lirong & Ma, Yizhong, 2019. "Availability and optimal maintenance policy for systems degrading in dynamic environments," European Journal of Operational Research, Elsevier, vol. 276(1), pages 133-143.
    13. Liu, Baoliang & Cui, Lirong & Wen, Yanqing & Shen, Jingyuan, 2013. "A performance measure for Markov system with stochastic supply patterns and stochastic demand patterns," Reliability Engineering and System Safety, Elsevier, vol. 119(C), pages 294-299.
    14. Lirong Cui & Shijia Du & Aofu Zhang, 2014. "Reliability measures for two-part partition of states for aggregated Markov repairable systems," Annals of Operations Research, Springer, vol. 212(1), pages 93-114, January.
    15. 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.
    16. Baoliang Liu & Lirong Cui & Yanqing Wen, 2014. "Interval reliability for aggregated Markov repairable system with repair time omission," Annals of Operations Research, Springer, vol. 212(1), pages 169-183, January.
    17. Chiacchio, F. & D’Urso, D. & Manno, G. & Compagno, L., 2016. "Stochastic hybrid automaton model of a multi-state system with aging: Reliability assessment and design consequences," Reliability Engineering and System Safety, Elsevier, vol. 149(C), pages 1-13.
    18. Lirong Cui & Quan Zhang & Dejing Kong, 2016. "Some New Concepts and Their Computational Formulae in Aggregated Stochastic Processes with Classifications Based on Sojourn Times," Methodology and Computing in Applied Probability, Springer, vol. 18(4), pages 999-1019, December.
    19. Gan, Shuyuan & Hu, Hengheng & Coit, David W., 2023. "Maintenance optimization considering the mutual dependence of the environment and system with decreasing effects of imperfect maintenance," Reliability Engineering and System Safety, Elsevier, vol. 235(C).
    20. Wu, Bei & Wei, Xiaohua & Zhang, Yamei & Bai, Sijun, 2023. "Modeling dynamic environment effects on dependent failure processes with varying failure thresholds," Reliability Engineering and System Safety, Elsevier, vol. 229(C).
    21. Li, Yan & Cui, Lirong & Lin, Cong, 2017. "Modeling and analysis for multi-state systems with discrete-time Markov regime-switching," Reliability Engineering and System Safety, Elsevier, vol. 166(C), pages 41-49.
    22. He Yi & Lirong Cui & Narayanaswamy Balakrishnan & Jingyuan Shen, 2022. "Multi-Point and Multi-Interval Bounded-Covering Availability Measures for Aggregated Markovian Repairable Systems," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2427-2453, December.
    23. Wei, Xiaohua & Bai, Sijun & Wu, Bei, 2023. "A novel shock-dependent preventive maintenance policy for degraded systems subject to dynamic environments and N-critical shocks," Reliability Engineering and System Safety, Elsevier, vol. 239(C).
    24. Cong Lin & Lirong Cui & David Coit & Min Lv, 2017. "An approximation method for evaluating the reliability of a dynamic k-out-of-n:F system subjected to cyclic alternating operation conditions," Journal of Risk and Reliability, , vol. 231(2), pages 109-120, April.
    25. Yi, He & Cui, Lirong & Balakrishnan, Narayanaswamy, 2021. "New reliability indices for first- and second-order discrete-time aggregated semi-Markov systems with an application to TT&C system," Reliability Engineering and System Safety, Elsevier, vol. 215(C).

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