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An Optimal Inspection and Replacement Policy under Incomplete State Information: Average Cost Criterion

  • Masamitsu Ohnishi
  • Hisashi Mine
  • Hajime Kawai
Conference paper
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 235)

Abstract

An optimal Inspection and replacement problem for a discrete-time Markovian deterioration system is investigated. It is assumed that the system is monitored incompletely by a certain mechanism which gives the decision-maker some Information about the exact state of the system. The problem is to obtain an optimal inspection and replacement policy minimizing the expected average cost per unit time over the infinite horizon and formulated as a partially observable Markov decision process. Under some reasonable conditions reflecting the practical meaning of the deterioration, it is shown that there exists an optimal Inspection and replacement policy in the class of monotonic four region-policies.

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References

  1. [1]
    C. Derman, “Optimal Replacement Rules when Changes of States are Markovian”, in Mathematical Optimization Technique, R. Bellman, Ed., Univ. of California Press, Berkley, California, 1963.Google Scholar
  2. [2]
    J. Eckles, “Optimum Maintenance with Incomplete Information”, Opns. Res., Vol. 16, 1968, pp. 1058–1067.CrossRefGoogle Scholar
  3. [3]
    S. Karlin, Total Positivity, Vol. 1, 1968, Stanford Univ. Press, Stanford, CaliforniazbMATHGoogle Scholar
  4. [4]
    G.E. Monahan, “A Survey of Partially Observable Markov Decision Process”, Man. Sci., Vol. 28, 1982, pp. 1–16.MathSciNetzbMATHGoogle Scholar
  5. [5]
    M. Ohnishi, H. Kawai and H. Mine, “An Optimal Inspection and Replace-Ment Policy under Incomplete State Information”,to appear.Google Scholar
  6. [6]
    D. Rosenfield, “Markovian Deterioration with Uncertain Information”, Opns. Res., Vol. 24, 1976, pp. 141–155.MathSciNetzbMATHCrossRefGoogle Scholar
  7. [7]
    T. Rockafellar, Convex Analysis, Princeton University Press, Princeton, New Jersey, 1970.zbMATHGoogle Scholar
  8. [8]
    S.M. Ross, “Arbitrary State Markovian Decision Processes”, Ann. Math. Stat., Vol. 39, 1968, pp. 2118–2122.zbMATHCrossRefGoogle Scholar
  9. [9]
    —, Applied Probability Models with Optimization Applications, Holden-day, San Francisco, California, 1970.zbMATHGoogle Scholar
  10. [10]
    —, “Quality Control under Markovian Deterioration”, Man. Sci., Vol. 17, 1971, PP. 587–596.zbMATHGoogle Scholar
  11. [11]
    E. Sondik, “The Optimal Control of Partially Observable Markov Processes over the Infinite Horizon”, Opns. Res., Vol.26, 1978, pp. 282–304.MathSciNetzbMATHCrossRefGoogle Scholar
  12. [12]
    C. White, “Optimal Inspection and Repair of a Production Process Subject to Deterioration”, J. Opns. Res. Soc., Vol. 29, 1978, pp. 235–243.zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  • Masamitsu Ohnishi
    • 1
  • Hisashi Mine
    • 1
  • Hajime Kawai
    • 2
  1. 1.Department of Applied Mathematics and Physics Faculty of EngineeringKyoto UniversityKyoto 606Japan
  2. 2.Department of Business Administration School of EconomicsUniversity of Osaka PrefectureOsaka 591Japan

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