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On the Maintenance of Systems Composed of Highly Reliable Components

Author

Listed:
  • Michael N. Katehakis

    (Department of Industrial Engineering, Technical University of Crete, Hania 73100, Crete, Greece and Department of Industrial Engineering, Columbia University, New York, New York 10027)

  • Cyrus Derman

    (Department of Industrial Engineering, Columbia University, New York, New York 10027)

Abstract

We consider the dynamic repair allocation problem for a general multi-component system that is maintained by a limited number of repairmen. Component functioning and repair times are exponentially distributed random variables with known parameters. At most one repairman may be assigned to a failed component and it is possible to reassign a repairman from one failed component to another instantaneously. The objective is to determine repair allocation policies that maximize a measure of performance of the system such as the expected discounted system operation time or the availability of the system. We consider systems composed of highly reliable, i.e., small failure rates, components and study asymptotic techniques for the determination of optimal policies. In the final section we find asymptotically optimal policies for the series, parallel, and a system composed of parallel subsystems connected in series.

Suggested Citation

  • Michael N. Katehakis & Cyrus Derman, 1989. "On the Maintenance of Systems Composed of Highly Reliable Components," Management Science, INFORMS, vol. 35(5), pages 551-560, May.
    • Handle: RePEc:inm:ormnsc:v:35:y:1989:i:5:p:551-560
    DOI: 10.1287/mnsc.35.5.551
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    Cited by:

    1. Xindan Li & Dan Tang & Yongjin Wang & Xuewei Yang, 2014. "Optimal processing rate and buffer size of a jump-diffusion processing system," Annals of Operations Research, Springer, vol. 217(1), pages 319-335, June.
    2. Apostolos Burnetas, 2013. "Customer equilibrium and optimal strategies in Markovian queues in series," Annals of Operations Research, Springer, vol. 208(1), pages 515-529, September.
    3. Mark Brown, 2013. "Sharp bounds for NBUE distributions," Annals of Operations Research, Springer, vol. 208(1), pages 245-250, September.
    4. Tomás Prieto-Rumeau & Onésimo Hernández-Lerma, 2016. "Uniform ergodicity of continuous-time controlled Markov chains: A survey and new results," Annals of Operations Research, Springer, vol. 241(1), pages 249-293, June.
    5. Michael Katehakis & Ingram Olkin & Sheldon Ross & Jian Yang, 2013. "On the life and work of Cyrus Derman," Annals of Operations Research, Springer, vol. 208(1), pages 5-26, September.
    6. Galbreath, Jeremy, 2017. "Drivers Of Environmental Sustainability In Wine Firms: The Role And Effect Of Women In Leadership," Working Papers 253851, American Association of Wine Economists.
    7. J. Boland & J. A. Filar & G. Mohammadian & A. Nazari, 2016. "Australian electricity market and price volatility," Annals of Operations Research, Springer, vol. 241(1), pages 357-372, June.
    8. Odysseas Kanavetas & Barış Balcıog̃lu, 2022. "The “Sensitive” Markovian queueing system and its application for a call center problem," Annals of Operations Research, Springer, vol. 317(2), pages 651-664, October.
    9. Ger Koole & Olaf Passchier, 1997. "Optimal control in light traffic Markov decision processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 45(1), pages 63-79, February.

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