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Optimal Repair of a Series System

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  • Donald R. Smith

    (Columbia University, New York, New York)

Abstract

A single repairman maintains a series system whose components have exponential failure and repair distributions. It is desired to assign the repairman to maximize the expected total discounted working time or average working time for the system. Whenever the failure rates of all components are equal, the time to repair the system from any initial state is stochastically independent of the operating policy. The Laplace transform of time to repair the system and the long-run average time that the system works are explicitly available. For the two-component series system the repair time is stochastically minimized if the failed component with longest expected lifetime is always under repair. This is true even if the repairman experiences random periods of time during which repair is not allowed. For an n -component series system the policy that always repairs the failed component with longest expected lifetime stochastically minimizes the repair time over the class of policies, that repair failed components in a predetermined order. We apply the results to a queuing system.

Suggested Citation

  • Donald R. Smith, 1978. "Optimal Repair of a Series System," Operations Research, INFORMS, vol. 26(4), pages 653-662, August.
    • Handle: RePEc:inm:oropre:v:26:y:1978:i:4:p:653-662
    DOI: 10.1287/opre.26.4.653
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    Cited by:

    1. Koole, Ger, 1995. "Optimal repairman assignment in two symmetric maintenance models," European Journal of Operational Research, Elsevier, vol. 82(2), pages 295-301, April.
    2. Frostig, Esther, 1999. "Jointly optimal allocation of a repairman and optimal control of service rate for machine repairman problem," European Journal of Operational Research, Elsevier, vol. 116(2), pages 274-280, July.
    3. Sheldon M. Ross, 2015. "A sequential scheduling problem with impatient jobs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(8), pages 659-663, December.

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