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Periodic replacement when minimal repair costs vary with time

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  • Philip J. Boland

Abstract

A policy of periodic replacement with minimal repair at failure is considered for a complex system. Under such a policy the system is replaced at multiples of some period T while minimal repair is performed at any intervening system failures. The cost of a minimal repair to the system is assumed to be a nonde‐creasing function of its age. A simple expression is derived for the expected minimal repair cost in an interval in terms of the cost function and the failure rate of the system. Necessary and sufficient conditions for the existence of an optimal replacement interval are exhibited in the case where the system life distribution is strictly increasing failure rate (IFR).

Suggested Citation

  • Philip J. Boland, 1982. "Periodic replacement when minimal repair costs vary with time," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 29(4), pages 541-546, December.
    • Handle: RePEc:wly:navlog:v:29:y:1982:i:4:p:541-546
    DOI: 10.1002/nav.3800290402
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    Cited by:

    1. Sheu, Shey-Huei & Liu, Tzu-Hsin & Zhang, Zhe-George, 2019. "Extended optimal preventive replacement policies with random working cycle," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 398-415.
    2. Li Li & Yong Wang & Kuo-Yi Lin, 2021. "Preventive maintenance scheduling optimization based on opportunistic production-maintenance synchronization," Journal of Intelligent Manufacturing, Springer, vol. 32(2), pages 545-558, February.
    3. Tzvi Goldstein & Shaul P. Ladany & Abraham Mehrez, 1988. "A discounted machine‐replacement model with an expected future technological breakthrough," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(2), pages 209-220, April.
    4. Maxim Finkelstein & Gregory Levitin, 2018. "Optimal Mission Duration for Partially Repairable Systems Operating in a Random Environment," Methodology and Computing in Applied Probability, Springer, vol. 20(2), pages 505-516, June.
    5. Xiao‐Gao Liu & Viliam Makis & Andrew K. S. Jardine, 1995. "A replacement model with overhauls and repairs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(7), pages 1063-1079, October.
    6. Fu, Yuqiang & Zhu, Xiaoyan & Ma, Xiaoyang, 2020. "Optimum component reallocation and system replacement maintenance for a used system with increasing minimal repair cost," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    7. H. W. Block & W. S. Borges & T. H. Savits, 1988. "A general age replacement model with minimal repair," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(5), pages 365-372, October.
    8. Yen-Luan Chen & Chin-Chih Chang & Dwan-Fang Sheu, 2016. "Optimum random and age replacement policies for customer-demand multi-state system reliability under imperfect maintenance," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(5), pages 1130-1141, April.
    9. Maxim Finkelstein & Gregory Levitin & Oleg A Stepanov, 2019. "On operation termination for degrading systems with two types of failures," Journal of Risk and Reliability, , vol. 233(3), pages 419-426, June.
    10. 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.
    11. Hoang Pham & Hongzhou Wang, 2000. "Optimal (τ, T) opportunistic maintenance of a k‐out‐of‐n:G system with imperfect PM and partial failure," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(3), pages 223-239, April.
    12. Maxim Finkelstein & Mahmood Shafiee, 2017. "Preventive maintenance for systems with repairable minor failures," Journal of Risk and Reliability, , vol. 231(2), pages 101-108, April.
    13. Ciriaco Valdez‐Flores & Richard M. Feldman, 1989. "A survey of preventive maintenance models for stochastically deteriorating single‐unit systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 36(4), pages 419-446, August.

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