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A multi-state shock model with mutative failure patterns

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Listed:
  • Zhao, Xian
  • Wang, Siqi
  • Wang, Xiaoyue
  • Cai, Kui

Abstract

In this paper, to accommodate the known fact that a multi-state system is more likely to fail when its state gets worse, a multi-state shock model is proposed, in which the system failure patterns are mutative for different states. Shocks are classified into type I, type II and type III by magnitude. A type III shock has a destructive effect on the system and causes a complete failure whenever it occurs. A type II shock triggers the system down to a lower state. The system completely fails when the additive number of type II shocks exceeds a threshold. A type I shock has different effects for different system states. The system completely fails if the cumulative number of type I shocks exceeds a threshold which decreases as the system state gets lower. Distributions of the lasting time until the end of each system state, the lifetime and the residual lifetime of the system are derived when the interarrival times between successive shocks follow a common continuous phase-type distribution. Three different replacement policies are proposed to fit the characteristic of the new model, and corresponding optimization models are constructed to gain the optimal quantities.

Suggested Citation

  • Zhao, Xian & Wang, Siqi & Wang, Xiaoyue & Cai, Kui, 2018. "A multi-state shock model with mutative failure patterns," Reliability Engineering and System Safety, Elsevier, vol. 178(C), pages 1-11.
    • Handle: RePEc:eee:reensy:v:178:y:2018:i:c:p:1-11
    DOI: 10.1016/j.ress.2018.05.014
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    References listed on IDEAS

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    1. Eryilmaz, Serkan, 2015. "Assessment of a multi-state system under a shock model," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 1-8.
    2. Toshio Nakagawa, 2007. "Shock and Damage Models in Reliability Theory," Springer Series in Reliability Engineering, Springer, number 978-1-84628-442-7, June.
    3. Rafiee, Koosha & Feng, Qianmei & Coit, David W., 2017. "Reliability assessment of competing risks with generalized mixed shock models," Reliability Engineering and System Safety, Elsevier, vol. 159(C), pages 1-11.
    4. Baggio, Michele & Perrings, Charles, 2015. "Modeling adaptation in multi-state resource systems," Ecological Economics, Elsevier, vol. 116(C), pages 378-386.
    5. Zhai, Qingqing & Ye, Zhi-Sheng & Yang, Jun & Zhao, Yu, 2016. "Measurement errors in degradation-based burn-in," Reliability Engineering and System Safety, Elsevier, vol. 150(C), pages 126-135.
    6. Zhao, Xian & Guo, Xiaoxin & Wang, Xiaoyue, 2018. "Reliability and maintenance policies for a two-stage shock model with self-healing mechanism," Reliability Engineering and System Safety, Elsevier, vol. 172(C), pages 185-194.
    7. Jian-Ming Bai & Zhe Zhang & Ze-Hui Li, 2014. "Lifetime properties of a cumulative shock model with a cluster structure," Annals of Operations Research, Springer, vol. 212(1), pages 21-41, January.
    8. Peng, Rui & Mo, Huadong & Xie, Min & Levitin, Gregory, 2013. "Optimal structure of multi-state systems with multi-fault coverage," Reliability Engineering and System Safety, Elsevier, vol. 119(C), pages 18-25.
    9. Yang, Li & Ma, Xiaobing & Peng, Rui & Zhai, Qingqing & Zhao, Yu, 2017. "A preventive maintenance policy based on dependent two-stage deterioration and external shocks," Reliability Engineering and System Safety, Elsevier, vol. 160(C), pages 201-211.
    10. Eryilmaz, Serkan, 2017. "δ-shock model based on Polya process and its optimal replacement policy," European Journal of Operational Research, Elsevier, vol. 263(2), pages 690-697.
    11. Cirillo, Pasquale & Hüsler, Jürg, 2011. "Extreme shock models: An alternative perspective," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 25-30, January.
    12. Gregory Levitin, 2011. "Reliability of multi-state systems with common bus performance sharing," IISE Transactions, Taylor & Francis Journals, vol. 43(7), pages 518-524.
    13. Cha, Ji Hwan & Finkelstein, Maxim & Levitin, Gregory, 2018. "Bivariate preventive maintenance of systems with lifetimes dependent on a random shock process," European Journal of Operational Research, Elsevier, vol. 266(1), pages 122-134.
    14. Fan, Mengfei & Zeng, Zhiguo & Zio, Enrico & Kang, Rui, 2017. "Modeling dependent competing failure processes with degradation-shock dependence," Reliability Engineering and System Safety, Elsevier, vol. 165(C), pages 422-430.
    15. Yuan-Jian Yang & Weiwen Peng & Debiao Meng & Shun-Peng Zhu & Hong-Zhong Huang, 2014. "Reliability analysis of direct drive electrohydraulic servo valves based on a wear degradation process and individual differences," Journal of Risk and Reliability, , vol. 228(6), pages 621-630, December.
    16. Kvassay, Miroslav & Zaitseva, Elena & Levashenko, Vitaly, 2017. "Importance analysis of multi-state systems based on tools of logical differential calculus," Reliability Engineering and System Safety, Elsevier, vol. 165(C), pages 302-316.
    17. Zhou, Xiaojun & Wu, Changjie & Li, Yanting & Xi, Lifeng, 2016. "A preventive maintenance model for leased equipment subject to internal degradation and external shock damage," Reliability Engineering and System Safety, Elsevier, vol. 154(C), pages 1-7.
    18. Gut, Allan & Hüsler, Jürg, 2005. "Realistic variation of shock models," Statistics & Probability Letters, Elsevier, vol. 74(2), pages 187-204, September.
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