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Optimal policies for cumulative damage models with maintenance last and first

Author

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  • Zhao, Xufeng
  • Qian, Cunhua
  • Nakagawa, Toshio

Abstract

From the economical viewpoint of several combined PM policies in reliability theory, this paper takes up a standard cumulative damage model in which the notion of maintenance last is applied, i.e., the unit undergoes preventive maintenances before failure at a planned time T, at a damage level Z, or at a shock number N, whichever occurs last. Expected cost rates are detailedly formulated, and optimal problems of two alternative policies which combine time-based with condition-based preventive maintenances are discussed, i.e., optimal TLâ Ž for N, ZLâ Ž for T, and NLâ Ž for T are rigorously obtained. Comparison methods between such maintenance last and conventional maintenance first are explored. It is determined theoretically and numerically which policy should be adopted, according to the different methods in different cases when the time-based or the condition-based PM policy is optimized.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:reensy:v:110:y:2013:i:c:p:50-59
    DOI: 10.1016/j.ress.2012.09.004
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    References listed on IDEAS

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    Cited by:

    1. Junyuan Wang & Jimin Ye & Liang Wang, 2022. "Extended age maintenance models and its optimization for series and parallel systems," Annals of Operations Research, Springer, vol. 312(1), pages 495-517, May.
    2. Zhao, Xufeng & Liu, Hu-Chen & Nakagawa, Toshio, 2015. "Where does “whichever occurs first†hold for preventive maintenance modelings?," Reliability Engineering and System Safety, Elsevier, vol. 142(C), pages 203-211.
    3. Sheu, Shey-Huei & Liu, Tzu-Hsin & Zhang, Zhe-George, 2019. "Extended optimal preventive replacement policies with random working cycle," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 398-415.
    4. Tsai, Hsin-Nan & Sheu, Shey-Huei & Zhang, Zhe George, 2017. "A trivariate optimal replacement policy for a deteriorating system based on cumulative damage and inspections," Reliability Engineering and System Safety, Elsevier, vol. 160(C), pages 122-135.
    5. Xufeng Zhao & Toshio Nakagawa, 2015. "Optimal periodic and random inspections with first, last and overtime policies," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(9), pages 1648-1660, July.
    6. Yang, Li & Zhao, Yu & Peng, Rui & Ma, Xiaobing, 2018. "Hybrid preventive maintenance of competing failures under random environment," Reliability Engineering and System Safety, Elsevier, vol. 174(C), pages 130-140.
    7. Nizar Mannai & Soufiane Gasmi, 2020. "Optimal design of k-out-of-n system under first and last replacement in reliability theory," Operational Research, Springer, vol. 20(3), pages 1353-1368, September.
    8. Sheu, Shey-Huei & Liu, Tzu-Hsin & Sheu, Wei-Teng & Zhang, Zhe-George & Ke, Jau-Chuan, 2021. "Optimal replacement policy with replacement last under cumulative damage models," Reliability Engineering and System Safety, Elsevier, vol. 209(C).
    9. Tsai, Hsin-Nan & Sheu, Shey-Huei & Zhang, Zhe George, 2017. "A trivariate optimal replacement policy for a deteriorating system based on cumulative damage and inspections," Reliability Engineering and System Safety, Elsevier, vol. 160(C), pages 74-88.
    10. 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.
    11. Hamidi, Maryam & Szidarovszky, Ferenc & Szidarovszky, Miklos, 2016. "New one cycle criteria for optimizing preventive replacement policies," Reliability Engineering and System Safety, Elsevier, vol. 154(C), pages 42-48.
    12. Phalguni Nanda & Prajamitra Bhuyan & Anup Dewanji, 2022. "Optimal replacement policy under cumulative damage model and strength degradation with applications," Annals of Operations Research, Springer, vol. 315(2), pages 1345-1371, August.
    13. Sheu, Shey-Huei & Tsai, Hsin-Nan & Sheu, Uan-Yu & Zhang, Zhe George, 2019. "Optimal replacement policies for a system based on a one-cycle criterion," Reliability Engineering and System Safety, Elsevier, vol. 191(C).

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