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Optimal Replacement and Maintenance Under Markovian Deterioration with Probability Bounds on Failure

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  • Cyrus Derman

    (Columbia University and Technion, Israel Institute of Technology)

Abstract

A system is observed periodically and classified into one of a finite number of states. On the basis of the observations certain maintenance or replacement decisions are made. Transitions probabilities from state to state are determined by the decisions. The problem considered is that of finding the decision rule which maximizes the expected length of time between replacements subject to the side conditions that the probabilities of replacement through certain undesirable states are bounded by prescribed numbers.

Suggested Citation

  • Cyrus Derman, 1963. "Optimal Replacement and Maintenance Under Markovian Deterioration with Probability Bounds on Failure," Management Science, INFORMS, vol. 9(3), pages 478-481, April.
    • Handle: RePEc:inm:ormnsc:v:9:y:1963:i:3:p:478-481
    DOI: 10.1287/mnsc.9.3.478
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    Cited by:

    1. Panagiotidou, S. & Tagaras, G., 2012. "Optimal integrated process control and maintenance under general deterioration," Reliability Engineering and System Safety, Elsevier, vol. 104(C), pages 58-70.
    2. Oguzhan Alagoz & Lisa M. Maillart & Andrew J. Schaefer & Mark S. Roberts, 2007. "Determining the Acceptance of Cadaveric Livers Using an Implicit Model of the Waiting List," Operations Research, INFORMS, vol. 55(1), pages 24-36, February.
    3. Deep, Akash & Zhou, Shiyu & Veeramani, Dharmaraj & Chen, Yong, 2023. "Partially observable Markov decision process-based optimal maintenance planning with time-dependent observations," European Journal of Operational Research, Elsevier, vol. 311(2), pages 533-544.
    4. 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.
    5. Wang, Kung-Jeng & Nguyen, Phuc Hong, 2017. "Capacity planning with technology replacement by stochastic dynamic programming," European Journal of Operational Research, Elsevier, vol. 260(2), pages 739-750.
    6. Oguzhan Alagoz & Lisa M. Maillart & Andrew J. Schaefer & Mark S. Roberts, 2004. "The Optimal Timing of Living-Donor Liver Transplantation," Management Science, INFORMS, vol. 50(10), pages 1420-1430, October.
    7. Oguzhan Alagoz & Lisa M. Maillart & Andrew J. Schaefer & Mark S. Roberts, 2007. "Choosing Among Living-Donor and Cadaveric Livers," Management Science, INFORMS, vol. 53(11), pages 1702-1715, November.
    8. Su, Chao-Ton & Wu, Sung-Chi & Chang, Cheng-Chang, 2000. "Multiaction maintenance subject to action-dependent risk and stochastic failure," European Journal of Operational Research, Elsevier, vol. 125(1), pages 133-148, August.

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