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Markovian Deterioration With Uncertain Information — A More General Model

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  • Donald Rosenfield

Abstract

A model of a deteriorating system with imperfect information is considered. The structures appropriate for such a model include failing machinery and depleted inventory systems. In an effort to add a new dimension to such models, it is assumed that the operator must pay an inspection cost to determine the precise state of the system. At the start of every time period, the operator is faced with three choices: repair, no action, or inspection. Under fairly general assumptions, the optimal policy for repair is found to be straightforward and intuitive. This result has two important areas of application.

Suggested Citation

  • Donald Rosenfield, 1976. "Markovian Deterioration With Uncertain Information — A More General Model," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 23(3), pages 389-405, September.
    • Handle: RePEc:wly:navlog:v:23:y:1976:i:3:p:389-405
    DOI: 10.1002/nav.3800230303
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    Cited by:

    1. 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.
    2. Wooseung Jang & J. George Shanthikumar, 2002. "Stochastic allocation of inspection capacity to competitive processes," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(1), pages 78-94, February.
    3. Wallace J. Hopp & Sung‐Chi Wu, 1988. "Multiaction maintenance under markovian deterioration and incomplete state information," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(5), pages 447-462, October.
    4. Wallace J. Hopp & Yar‐Lin Kuo, 1998. "An optimal structured policy for maintenance of partially observable aircraft engine components," Naval Research Logistics (NRL), John Wiley & Sons, vol. 45(4), pages 335-352, June.
    5. Junbo Son & Yeongin Kim & Shiyu Zhou, 2022. "Alerting patients via health information system considering trust-dependent patient adherence," Information Technology and Management, Springer, vol. 23(4), pages 245-269, December.
    6. Stephen M. Gilbert & Hena M Bar, 1999. "The value of observing the condition of a deteriorating machine," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(7), pages 790-808, October.
    7. Bismut, Elizabeth & Straub, Daniel, 2021. "Optimal adaptive inspection and maintenance planning for deteriorating structural systems," Reliability Engineering and System Safety, Elsevier, vol. 215(C).
    8. Lisa M. Maillart & Ludmila Zheltova, 2007. "Structured maintenance policies on interior sample paths," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(6), pages 645-655, September.
    9. Armando Z. Milioni & Stanley R. Pliska, 1988. "Optimal inspection under semi‐markovian deterioration: Basic results," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(5), pages 373-392, October.
    10. Miehling, Erik & Teneketzis, Demosthenis, 2020. "Monotonicity properties for two-action partially observable Markov decision processes on partially ordered spaces," European Journal of Operational Research, Elsevier, vol. 282(3), pages 936-944.
    11. Ramin Moghaddass & Şeyda Ertekin, 2018. "Joint optimization of ordering and maintenance with condition monitoring data," Annals of Operations Research, Springer, vol. 263(1), pages 271-310, April.
    12. Chiel van Oosterom & Lisa M. Maillart & Jeffrey P. Kharoufeh, 2017. "Optimal maintenance policies for a safety‐critical system and its deteriorating sensor," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(5), pages 399-417, August.
    13. Hao Zhang & Weihua Zhang, 2023. "Analytical Solution to a Partially Observable Machine Maintenance Problem with Obvious Failures," Management Science, INFORMS, vol. 69(7), pages 3993-4015, July.

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