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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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