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Optimal number of minimal repairs with cumulative repair cost limit for a two-unit system with failure rate interactions

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  • Min-Tsai Lai
  • Huey Yan

Abstract

A discrete replacement model is presented that includes a cumulative repair cost limit for a two-unit system with failure rate interactions between the units. We assume a failure in unit 1 causes the failure rate in unit 2 to increase, whereas a failure in unit 2 causes a failure in unit 1, resulting in a total system failure. If unit 1 fails and the cumulative repair cost till to this failure is less than a limit L, then unit 1 is repaired. If there is a failure in unit 1 and the cumulative repair cost exceeds L or the number of failures equals n, the entire system is preventively replaced. The system is also replaced at a total failure, and such replacement cost is higher than the preventive replacement cost. The long-term expected cost per unit time is derived using the expected costs as the optimality criterion. The minimum-cost policy is derived, and existence and uniqueness are proved.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:tsysxx:v:47:y:2016:i:2:p:466-473
    DOI: 10.1080/00207721.2014.886749
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    References listed on IDEAS

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    1. 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.
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    3. Chien-Kuo Sung & Shey-Huei Sheu & Tsung-Shin Hsu & Yan-Chun Chen, 2013. "Extended optimal replacement policy for a two-unit system with failure rate interaction and external shocks," International Journal of Systems Science, Taylor & Francis Journals, vol. 44(5), pages 877-888.
    4. Cho, Danny I. & Parlar, Mahmut, 1991. "A survey of maintenance models for multi-unit systems," European Journal of Operational Research, Elsevier, vol. 51(1), pages 1-23, March.
    5. Murthy, D. N. P. & Nguyen, D. G., 1985. "Study of a multi-component system with failure interaction," European Journal of Operational Research, Elsevier, vol. 21(3), pages 330-338, September.
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