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Reliability analysis of Markov history-dependent repairable systems with neglected failures

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  • Du, Shijia
  • Zeng, Zhiguo
  • Cui, Lirong
  • Kang, Rui

Abstract

Markov history-dependent repairable systems refer to the Markov repairable systems in which some states are changeable and dependent on recent evolutional history of the system. In practice, many Markov history-dependent repairable systems are subjected to neglected failures, i.e., some failures do not affect system performances if they can be repaired promptly. In this paper, we develop a model based on the theory of aggregated stochastic processes to describe the history-dependent behavior and the effect of neglected failures on the Markov history-dependent repairable systems. Based on the developed model, instantaneous and steady-state availabilities are derived to characterize the reliability of the system. Four reliability-related time distributions, i.e., distribution for the k th working period, distribution for the k th failure period, distribution for the real working time in an effective working period, distribution for the neglected failure time in an effective working period, are also derived to provide a more comprehensive description of the system's reliability. Thanks to the power of the theory of aggregated stochastic processes, closed-form expressions are obtained for all the reliability indexes and time distributions. Finally, the developed indexes and analysis methods are demonstrated by a numerical example.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:reensy:v:159:y:2017:i:c:p:134-142
    DOI: 10.1016/j.ress.2016.10.030
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    References listed on IDEAS

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    2. Liying Wang & Lirong Cui, 2013. "Performance Evaluation Of Aggregated Markov Repairable Systems With Multi-Operating Levels," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 30(04), pages 1-27.
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    4. Liu, Baoliang & Cui, Lirong & Wen, Yanqing & Shen, Jingyuan, 2015. "A cold standby repairable system with working vacations and vacation interruption following Markovian arrival process," Reliability Engineering and System Safety, Elsevier, vol. 142(C), pages 1-8.
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    6. Shijia Du & Cong Lin & Lirong Cui, 2016. "Reliabilities of a single-unit system with multi-phased missions," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(9), pages 2524-2537, May.
    7. Lu, Ji-Min & Wu, Xiao-Yue & Liu, Yiliu & Ann Lundteigen, Mary, 2015. "Reliability analysis of large phased-mission systems with repairable components based on success-state sampling," Reliability Engineering and System Safety, Elsevier, vol. 142(C), pages 123-133.
    8. 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.
    9. 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.
    10. Csenki, Attila, 2007. "Joint interval reliability for Markov systems with an application in transmission line reliability," Reliability Engineering and System Safety, Elsevier, vol. 92(6), pages 685-696.
    11. 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.
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    Cited by:

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    3. Jia, Heping & Liu, Dunnan & Li, Yanbin & Ding, Yi & Liu, Mingguang & Peng, Rui, 2020. "Reliability evaluation of power systems with multi-state warm standby and multi-state performance sharing mechanism," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    4. 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.
    5. Dong, Wenjie & Liu, Sifeng & Tao, Liangyan & Cao, Yingsai & Fang, Zhigeng, 2019. "Reliability variation of multi-state components with inertial effect of deteriorating output performances," Reliability Engineering and System Safety, Elsevier, vol. 186(C), pages 176-185.
    6. Heping Jia & Rui Peng & Yi Ding & Yonghua Song, 2019. "Reliability of demand-based warm standby system with common bus performance sharing," Journal of Risk and Reliability, , vol. 233(4), pages 580-592, August.
    7. Jagtap, Hanumant P. & Bewoor, Anand K. & Kumar, Ravinder & Ahmadi, Mohammad Hossein & Chen, Lingen, 2020. "Performance analysis and availability optimization to improve maintenance schedule for the turbo-generator subsystem of a thermal power plant using particle swarm optimization," Reliability Engineering and System Safety, Elsevier, vol. 204(C).

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