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Optimum design and replacement policies for k-out-of-n systems with deviation time and cost

Author

Listed:
  • Junyuan Wang

    (China Jiliang University)

  • Xufeng Zhao

    (Nanjing University of Aeronautics and Astronautics
    Wenzhou University)

  • Jiawei Xiang

    (Wenzhou University)

Abstract

In this paper, a new repairable k-out-of-n system model is proposed, in which the deviation cost of the system is taken into account. Firstly, the standard k-out-of-n system is replaced at planned time or at the failure time. Next, replacement policies are studied at planned time or periodic time when k is a constant. Thirdly, replacement policies are studied at planned time or periodic time when k is a random number, respectively. Finally, replacement policies are planned at the completion of random working time. The expected cost rate functions and its optimum replacement policies are derived analytically for each model. Meanwhile, optimum number of units is designed. The analytical solution of replacement policies for each model is discussed. Numerical examples are given to demonstrate our results.

Suggested Citation

  • Junyuan Wang & Xufeng Zhao & Jiawei Xiang, 2024. "Optimum design and replacement policies for k-out-of-n systems with deviation time and cost," Annals of Operations Research, Springer, vol. 340(1), pages 593-617, September.
    • Handle: RePEc:spr:annopr:v:340:y:2024:i:1:d:10.1007_s10479-022-05043-1
    DOI: 10.1007/s10479-022-05043-1
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    References listed on IDEAS

    as
    1. Xufeng Zhao & Mingchih Chen & Toshio Nakagawa, 2022. "Periodic replacement policies with shortage and excess costs," Annals of Operations Research, Springer, vol. 311(1), pages 469-487, April.
    2. 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.
    3. 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.
    4. Mingchih Chen & Xufeng Zhao & Toshio Nakagawa, 2019. "Replacement policies with general models," Annals of Operations Research, Springer, vol. 277(1), pages 47-61, June.
    5. Toshio Nakagawa, 2008. "Advanced Reliability Models and Maintenance Policies," Springer Series in Reliability Engineering, Springer, number 978-1-84800-294-4, April.
    6. Ibrahim Yusuf, 2016. "Reliability modelling of a parallel system with a supporting device and two types of preventive maintenance," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 25(3), pages 269-287.
    7. Xufeng Zhao & Satoshi Mizutani & Mingchih Chen & Toshio Nakagawa, 2022. "Preventive replacement policies for parallel systems with deviation costs between replacement and failure," Annals of Operations Research, Springer, vol. 312(1), pages 533-551, May.
    8. 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.
    9. Leila Jafari & Farnoosh Naderkhani & Viliam Makis, 2018. "Joint optimization of maintenance policy and inspection interval for a multi-unit series system using proportional hazards model," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 69(1), pages 36-48, January.
    10. Hadi Akbarzade Khorshidi & Indra Gunawan & M. Yousef Ibrahim, 2015. "On Reliability Evaluation of Multistate Weighted -out-of- System Using Present Value," The Engineering Economist, Taylor & Francis Journals, vol. 60(1), pages 22-39, January.
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