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A note on replacement policy for a system subject to non-homogeneous pure birth shocks

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  • Sheu, Shey-Huei
  • Chang, Chin-Chih
  • Zhang, Zhe George
  • Chien, Yu-Hung

Abstract

A system is subject to shocks that arrive according to a non-homogeneous pure birth process. As shocks occur, the system has two types of failures. Type-I failure (minor failure) is removed by a general repair, whereas type-II failure (catastrophic failure) is removed by an unplanned replacement. The occurrence of the failure type is based on some random mechanism which depends on the number of shocks occurred since the last replacement. Under an age replacement policy, a planned (or scheduled) replacement happens whenever an operating system reaches age T. The aim of this note is to derive the expected cost functions and characterize the structure of the optimal replacement policy for such a general setting. We show that many previous models are special cases of our general model. A numerical example is presented to show the application of the algorithm and several useful insights.

Suggested Citation

  • Sheu, Shey-Huei & Chang, Chin-Chih & Zhang, Zhe George & Chien, Yu-Hung, 2012. "A note on replacement policy for a system subject to non-homogeneous pure birth shocks," European Journal of Operational Research, Elsevier, vol. 216(2), pages 503-508.
    • Handle: RePEc:eee:ejores:v:216:y:2012:i:2:p:503-508
    DOI: 10.1016/j.ejor.2011.07.056
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    References listed on IDEAS

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    Cited by:

    1. Levitin, Gregory & Finkelstein, Maxim & Dai, Yuanshun, 2020. "Mission abort and rescue for multistate systems operating under the Poisson process of shocks," Reliability Engineering and System Safety, Elsevier, vol. 202(C).
    2. Huang, Yeu-Shiang & Fang, Chih-Chiang & Lu, Chang-Ming & (Bill) Tseng, Tzu-Liang, 2022. "Optimal Warranty Policy for Consumer Electronics with Dependent Competing Failure Processes," Reliability Engineering and System Safety, Elsevier, vol. 222(C).
    3. Zhao, Xufeng & Qian, Cunhua & Nakagawa, Toshio, 2013. "Optimal policies for cumulative damage models with maintenance last and first," Reliability Engineering and System Safety, Elsevier, vol. 110(C), pages 50-59.
    4. 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.
    5. Chien, Yu-Hung, 2019. "The optimal preventive-maintenance policy for a NHPBP repairable system under free-repair warranty," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 444-453.
    6. Zhao, Xufeng & Al-Khalifa, Khalifa N. & Magid Hamouda, Abdel & Nakagawa, Toshio, 2017. "Age replacement models: A summary with new perspectives and methods," Reliability Engineering and System Safety, Elsevier, vol. 161(C), pages 95-105.
    7. Levitin, Gregory & Finkelstein, Maxim & Dai, Yuanshun, 2018. "Heterogeneous standby systems with shocks-driven preventive replacements," European Journal of Operational Research, Elsevier, vol. 266(3), pages 1189-1197.
    8. Shey-Huei Sheu & Tzu-Hsin Liu & Zhe-George Zhang & Hsin-Nan Tsai & Jung-Chih Chen, 2016. "Optimal two-threshold replacement policy in a cumulative damage model," Annals of Operations Research, Springer, vol. 244(1), pages 23-47, September.
    9. 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.
    10. Zhao, Xufeng & Nakagawa, Toshio, 2012. "Optimization problems of replacement first or last in reliability theory," European Journal of Operational Research, Elsevier, vol. 223(1), pages 141-149.

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