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Optimal inspection under semi‐markovian deterioration: Basic results

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  • Armando Z. Milioni
  • Stanley R. Pliska

Abstract

This article develops a model for determining the optimal inspection schedule for a system which deteriorates according to a semi‐Markov process that progresses through three states: good, defective, and bad. A binary test is used, and false positives may occur. A true positive results in an action that reduces the likelihood of entering the bad state, but at most one such corrective action can occur during the lifetime of the system. Costs are associated with each inspection, each false positive, the corrective action, and the entrance into the bad state. Dynamic programming is used to compute the minimum expected cost, which is a function of the age of the system. The optimal inspection schedule is readily derived from this value function. Computational examples are provided. This model is appropriate for medical screening or for a mission where there is only one spare part.

Suggested Citation

  • 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.
    • Handle: RePEc:wly:navres:v:35:y:1988:i:5:p:373-392
    DOI: 10.1002/1520-6750(198810)35:53.0.CO;2-W
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    References listed on IDEAS

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    1. Donald Rosenfield, 1976. "Markovian Deterioration with Uncertain Information," Operations Research, INFORMS, vol. 24(1), pages 141-155, February.
    2. S. Christian Albright, 1979. "Structural Results for Partially Observable Markov Decision Processes," Operations Research, INFORMS, vol. 27(5), pages 1041-1053, October.
    3. Richard D. Smallwood & Edward J. Sondik, 1973. "The Optimal Control of Partially Observable Markov Processes over a Finite Horizon," Operations Research, INFORMS, vol. 21(5), pages 1071-1088, October.
    4. 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.
    5. Chelsea C. White, 1977. "A Markov Quality Control Process Subject to Partial Observation," Management Science, INFORMS, vol. 23(8), pages 843-852, April.
    6. George E. Monahan, 1982. "State of the Art---A Survey of Partially Observable Markov Decision Processes: Theory, Models, and Algorithms," Management Science, INFORMS, vol. 28(1), pages 1-16, January.
    7. Edward J. Sondik, 1978. "The Optimal Control of Partially Observable Markov Processes over the Infinite Horizon: Discounted Costs," Operations Research, INFORMS, vol. 26(2), pages 282-304, April.
    8. S. Christian Albright, 1980. "Optimal maintenance‐repair policies for the machine repair problem," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 27(1), pages 17-27, March.
    9. Y. S. Sherif & M. L. Smith, 1981. "Optimal maintenance models for systems subject to failure–A Review," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 28(1), pages 47-74, March.
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