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Optimum Maintenance with Incomplete Information

Author

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  • James E. Eckles

    (The Rand Corporation, Santa Monica, California 90406)

Abstract

The maintenance of a system characterized by a discrete-parameter, non-stationary, finite-state Markov process is considered. Prior to each transition the decision maker selects one of a finite number of available actions (replacements, repairs, inspections, etc.) on the basis of a time sequence of noisy state measurements. The action selected and the system's age determine the subsequent one-step transition probabilities and the conditional (on the system states) distributions of the next measurement. Costs dependent on the action selected, the system's state, and age are assigned to each possible transition. It is shown that the action that minimizes the discounted value of expected immediate and future costs (assuming optimum future actions) is determined by the system's age and the posterior distribution over the states. With this result a dynamic-programming method is presented for the calculation of optimum maintenance policies.

Suggested Citation

  • James E. Eckles, 1968. "Optimum Maintenance with Incomplete Information," Operations Research, INFORMS, vol. 16(5), pages 1058-1067, October.
    • Handle: RePEc:inm:oropre:v:16:y:1968:i:5:p:1058-1067
    DOI: 10.1287/opre.16.5.1058
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    Citations

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    Cited by:

    1. Viliam Makis, 2008. "Multivariate Bayesian Control Chart," Operations Research, INFORMS, vol. 56(2), pages 487-496, April.
    2. Makis, Viliam, 2009. "Multivariate Bayesian process control for a finite production run," European Journal of Operational Research, Elsevier, vol. 194(3), pages 795-806, May.
    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. Hao Zhang, 2010. "Partially Observable Markov Decision Processes: A Geometric Technique and Analysis," Operations Research, INFORMS, vol. 58(1), pages 214-228, February.
    5. L M Maillart & T G Yeung & Z Gozde Icten, 2011. "Selecting test sensitivity and specificity parameters to optimally maintain a degrading system," Journal of Risk and Reliability, , vol. 225(2), pages 131-139, June.
    6. Rafic Faddoul & Abdul-Hamid Soubra & Wassim Raphael & Alaa Chateauneuf, 2013. "Extension of dynamic programming models for management optimization from single structure to multi-structures level," Post-Print hal-01006860, HAL.
    7. 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.
    8. Andrei Sleptchenko & M. Eric Johnson, 2015. "Maintaining Secure and Reliable Distributed Control Systems," INFORMS Journal on Computing, INFORMS, vol. 27(1), pages 103-117, February.
    9. Faddoul, R. & Raphael, W. & Chateauneuf, A., 2018. "Maintenance optimization of series systems subject to reliability constraints," Reliability Engineering and System Safety, Elsevier, vol. 180(C), pages 179-188.
    10. Sait Tunç & Oguzhan Alagoz & Elizabeth S. Burnside, 2022. "A new perspective on breast cancer diagnostic guidelines to reduce overdiagnosis," Production and Operations Management, Production and Operations Management Society, vol. 31(5), pages 2361-2378, May.
    11. Liu, Xingchen & Sun, Qiuzhuang & Ye, Zhi-Sheng & Yildirim, Murat, 2021. "Optimal multi-type inspection policy for systems with imperfect online monitoring," Reliability Engineering and System Safety, Elsevier, vol. 207(C).
    12. 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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