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Markovian Deterioration with Uncertain Information

Author

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  • Donald Rosenfield

    (Stale University of New York, Stony Brook, New York)

Abstract

This paper presents a model of a deteriorating process with imperfect information. This model, unlike many previous efforts, stipulates that the operator most pay an inspection cost to determine the state of the system. This situation presents him with three choices at every time period: repair, inspection, or inaction. Under the assumptions that the transition matrix representing the process is upper-triangular and totally positive of order two, it is shown that the state-space can be broken up into at most four regions of action and that the optimal region of repair is of a special intuitive type.

Suggested Citation

  • Donald Rosenfield, 1976. "Markovian Deterioration with Uncertain Information," Operations Research, INFORMS, vol. 24(1), pages 141-155, February.
    • Handle: RePEc:inm:oropre:v:24:y:1976:i:1:p:141-155
    DOI: 10.1287/opre.24.1.141
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Jonathan E. Helm & Mariel S. Lavieri & Mark P. Van Oyen & Joshua D. Stein & David C. Musch, 2015. "Dynamic Forecasting and Control Algorithms of Glaucoma Progression for Clinician Decision Support," Operations Research, INFORMS, vol. 63(5), pages 979-999, October.
    9. Sarang Deo & Seyed Iravani & Tingting Jiang & Karen Smilowitz & Stephen Samuelson, 2013. "Improving Health Outcomes Through Better Capacity Allocation in a Community-Based Chronic Care Model," Operations Research, INFORMS, vol. 61(6), pages 1277-1294, December.
    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. A. Gürhan Kök & Kevin H. Shang, 2007. "Inspection and Replenishment Policies for Systems with Inventory Record Inaccuracy," Manufacturing & Service Operations Management, INFORMS, vol. 9(2), pages 185-205, February.
    12. 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.
    13. 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.
    14. 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.
    15. M. S. Krishnan & Tridas Mukhopadhyay & Charles H. Kriebel, 2004. "A Decision Model for Software Maintenance," Information Systems Research, INFORMS, vol. 15(4), pages 396-412, December.
    16. Michael Jong Kim & Viliam Makis, 2013. "Joint Optimization of Sampling and Control of Partially Observable Failing Systems," Operations Research, INFORMS, vol. 61(3), pages 777-790, June.
    17. 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.
    18. 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.
    19. Jue Wang & Chi-Guhn Lee, 2015. "Multistate Bayesian Control Chart Over a Finite Horizon," Operations Research, INFORMS, vol. 63(4), pages 949-964, August.
    20. Jang, Wooseung & Shanthikumar, J. George, 2004. "Sequential process control under capacity constraints," European Journal of Operational Research, Elsevier, vol. 155(3), pages 695-714, June.

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