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A geometric process repair model with inspections and its optimisation

Author

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  • G.Q. Cheng
  • L. Li

Abstract

In this article, a deteriorating simple repairable system with inspections, is studied. We assume that the system failure can only be detected by inspections and the repair of the system is not as good as new. Further assume that the successive working times of the system form a decreasing geometric process whereas the consecutive repair times form an increasing geometric process. Under these assumptions, we present a bivariate mixed policy (T, N), respectively, based on the time interval between two successive inspections and the failure-number of the system. Our aim is to determine an optimal mixed policy (T, N)* such that the long-run average cost per unit time (i.e. the average cost rate) is minimised. The explicit expression of the average cost rate is derived, and the corresponding optimal mixed policy can be determined numerically. Finally, we provide a numerical example to illustrate our model, and carry through some discussions and sensitivity analysis.

Suggested Citation

  • G.Q. Cheng & L. Li, 2012. "A geometric process repair model with inspections and its optimisation," International Journal of Systems Science, Taylor & Francis Journals, vol. 43(9), pages 1650-1655.
    • Handle: RePEc:taf:tsysxx:v:43:y:2012:i:9:p:1650-1655
    DOI: 10.1080/00207721.2010.549586
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    Citations

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    Cited by:

    1. Juan Eloy Ruiz-Castro, 2015. "A preventive maintenance policy for a standby system subject to internal failures and external shocks with loss of units," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(9), pages 1600-1613, July.
    2. Guan Jun Wang & Yuan Lin Zhang, 2016. "Optimal replacement policy for a two-dissimilar-component cold standby system with different repair actions," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(5), pages 1021-1031, April.
    3. Arnold, Richard & Chukova, Stefanka & Hayakawa, Yu & Marshall, Sarah, 2020. "Geometric-Like Processes: An Overview and Some Reliability Applications," Reliability Engineering and System Safety, Elsevier, vol. 201(C).
    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 74-88.
    5. Miaomiao Yu & Yinghui Tang, 2024. "Analyze periodic inspection and replacement policy of a shock and wear model with phase-type inter-shock arrival times using roots method," Journal of Risk and Reliability, , vol. 238(2), pages 233-246, April.
    6. 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.
    7. Wenke Gao, 2020. "An extended geometric process and its application in replacement policy," Journal of Risk and Reliability, , vol. 234(1), pages 88-103, February.
    8. 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.
    9. Shey-Huei Sheu & Hsin-Nan Tsai & Tsung-Shin Hsu & Fu-Kwun Wang, 2015. "Optimal number of minimal repairs before replacement of a deteriorating system with inspections," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(8), pages 1367-1379, June.
    10. Qinglai Dong & Lirong Cui & Hongda Gao, 2019. "A bivariate replacement policy for an imperfect repair system based on geometric processes," Journal of Risk and Reliability, , vol. 233(4), pages 670-681, August.
    11. Sheu, Shey-Huei & Tsai, Hsin-Nan & Wang, Fu-Kwun & Zhang, Zhe George, 2015. "An extended optimal replacement model for a deteriorating system with inspections," Reliability Engineering and System Safety, Elsevier, vol. 139(C), pages 33-49.

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