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Optimal number of minimal repairs before replacement of a deteriorating system with inspections

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  • Shey-Huei Sheu
  • Hsin-Nan Tsai
  • Tsung-Shin Hsu
  • Fu-Kwun Wang

Abstract

In this study, we propose a generalised replacement model for a deteriorating system with failures that could only be detected through inspection work. The system is assumed to have two types of failures and is replaced at the Nth type I failure (minor failure) or first type II failure (catastrophic failure), depending on whichever occurs first. The probability of type I and II failures depends on the number of failures since the last replacement. Such systems can be repaired upon type I failure, but are stochastically deteriorating, that is, the lengths of the operating intervals are stochastically decreasing, whereas the durations of the repairs are stochastically increasing. Then, the expected net cost rate is obtained. Some special cases are considered. Finally, a numerical example is provided.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:tsysxx:v:46:y:2015:i:8:p:1367-1379
    DOI: 10.1080/00207721.2013.822125
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    References listed on IDEAS

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    1. Wang, Wenbin, 2009. "An inspection model for a process with two types of inspections and repairs," Reliability Engineering and System Safety, Elsevier, vol. 94(2), pages 526-533.
    2. Shey‐Huei Sheu & William S. Griffith, 1996. "Optimal number of minimal repairs before replacement of a system subject to shocks," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(3), pages 319-333, April.
    3. 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.
    4. Laurence A. Baxter, 1982. "Reliability applications of the relevation transform," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 29(2), pages 323-330, June.
    5. Nakagawa, T. & Mizutani, S. & Chen, M., 2010. "A summary of periodic and random inspection policies," Reliability Engineering and System Safety, Elsevier, vol. 95(8), pages 906-911.
    6. Sheu, Shey-Huei, 1999. "Extended optimal replacement model for deteriorating systems," European Journal of Operational Research, Elsevier, vol. 112(3), pages 503-516, February.
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    Cited by:

    1. 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.
    2. Shey-Huei Sheu & Tzu-Hsin Liu & Wei-Teng Sheu & Yu-Hung Chien & Zhe-George Zhang, 2024. "Extended replacement policy for a system under shocks effect," Annals of Operations Research, Springer, vol. 340(1), pages 507-530, September.
    3. 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.

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