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Optimal age-replacement model with age-dependent type of failure and random lead time based on a cumulative repair-cost limit policy

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  • Yu-Hung Chien
  • Chin-Chih Chang
  • Shey-Huei Sheu

Abstract

In this paper, we consider an age-replacement model with minimal repair based on a cumulative repair cost limit and random lead time for replacement delivery. A cumulative repair cost limit policy uses information about a system’s entire repair cost history to decide whether the system is repaired or replaced; a random lead time models delay in delivery of a replacement once it is ordered. A general cost model is developed for the average cost per unit time based on the stochastic behavior of the assumed system, reflecting the costs of both storing a spare and of system downtime. The optimal age for preventive replacement minimizing that cost rate is derived, its existence and uniqueness is shown, and structural properties are presented. Various special cases are included, and a numerical example is given for illustration. Because the framework and analysis are general, the proposed model extends several existing results. Copyright Springer Science+Business Media, LLC 2010

Suggested Citation

  • Yu-Hung Chien & Chin-Chih Chang & Shey-Huei Sheu, 2010. "Optimal age-replacement model with age-dependent type of failure and random lead time based on a cumulative repair-cost limit policy," Annals of Operations Research, Springer, vol. 181(1), pages 723-744, December.
    • Handle: RePEc:spr:annopr:v:181:y:2010:i:1:p:723-744:10.1007/s10479-009-0679-0
    DOI: 10.1007/s10479-009-0679-0
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    References listed on IDEAS

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    1. Chien, Yu-Hung & Sheu, Shey-Huei & Zhang, Zhe George & Love, Ernie, 2006. "An extended optimal replacement model of systems subject to shocks," European Journal of Operational Research, Elsevier, vol. 175(1), pages 399-412, November.
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    Cited by:

    1. Xufeng Zhao & Toshio Nakagawa, 2016. "Over-time and over-level replacement policies with random working cycles," Annals of Operations Research, Springer, vol. 244(1), pages 103-116, September.
    2. Caiyun Niu & Xiaolin Liang & Bingfeng Ge & Xue Tian & Yingwu Chen, 2016. "Optimal replacement policy for a repairable system with deterioration based on a renewal-geometric process," Annals of Operations Research, Springer, vol. 244(1), pages 49-66, September.
    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. Min-Tsai Lai & Huey Yan, 2016. "Optimal number of minimal repairs with cumulative repair cost limit for a two-unit system with failure rate interactions," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(2), pages 466-473, January.
    5. Chien, Yu-Hung & Sheu, Shey-Huei & Zhang, Zhe George, 2012. "Optimal maintenance policy for a system subject to damage in a discrete time process," Reliability Engineering and System Safety, Elsevier, vol. 103(C), pages 1-10.
    6. Yonit Barron, 2018. "Group maintenance policies for an R-out-of-N system with phase-type distribution," Annals of Operations Research, Springer, vol. 261(1), pages 79-105, February.

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