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Optimal number of minimal repairs before replacement of a system subject to shocks

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  • Shey‐Huei Sheu
  • William S. Griffith

Abstract

A system is subject to shocks that arrive according to a nonhomogeneous Poisson process. As shocks occur a system has two types of failures. Type 1 failure (minor failure) is removed by a minimal repair, whereas type 2 failure (catastrophic failure) is removed by replacement. The probability of a type 2 failure is permitted to depend on the number of shocks since the last replacement. A system is replaced at the times of type 2 failure or at the nth type 1 failure, whichever comes first. The optimal policy is to select n* to minimize the expected cost per unit time for an infinite time span. A numerical example is given to illustrate the method. © 1996 John Wiley & Sons, Inc.

Suggested Citation

  • 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.
    • Handle: RePEc:wly:navres:v:43:y:1996:i:3:p:319-333
    DOI: 10.1002/(SICI)1520-6750(199604)43:33.0.CO;2-C
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    References listed on IDEAS

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    1. Dror Zuckerman, 1980. "A note on the optimal replacement time of damaged devices," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 27(3), pages 521-524, September.
    2. Sheu, Shey-Huei, 1993. "A generalized model for determining optimal number of minimal repairs before replacement," European Journal of Operational Research, Elsevier, vol. 69(1), pages 38-49, August.
    3. Prem S. Puri & Harshinder Singh, 1986. "Optimum Replacement of a System Subject to Shocks: A Mathematical Lemma," Operations Research, INFORMS, vol. 34(5), pages 782-789, October.
    4. Philip J. Boland & Frank Proschan, 1983. "Optimum Replacement of a System Subject to Shocks," Operations Research, INFORMS, vol. 31(4), pages 697-704, August.
    5. Richard Barlow & Larry Hunter, 1960. "Optimum Preventive Maintenance Policies," Operations Research, INFORMS, vol. 8(1), pages 90-100, February.
    6. Howard M. Taylor, 1975. "Optimal replacement under additive damage and other failure models," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 22(1), pages 1-18, March.
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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. Y-H Chien & C-C Chang & S-H Sheu, 2009. "Optimal periodical time for preventive replacement based on a cumulative repair-cost limit and random lead time," Journal of Risk and Reliability, , vol. 223(4), pages 333-345, December.
    3. 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.
    4. 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.
    5. Shey-Huei Sheu & Chin-Chih Chang & Yu-Hung Chien, 2011. "Optimal age-replacement time with minimal repair based on cumulative repair-cost limit for a system subject to shocks," Annals of Operations Research, Springer, vol. 186(1), pages 317-329, June.

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