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Optimal Replacement Rules when Changes of State are Semi-Markovian

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  • Edward P. C. Kao

    (Yale University, New Haven, Connecticut)

Abstract

This paper investigates the use of a discrete-time semi-Markov process to model a system that deteriorates in usage. Replacement rules that are (1) state-dependent, (2) state-age-dependent, and (3) age-dependent are proposed. The system operating costs and replacement costs are functions of the underlying states. The optimization criterion is the expected average cost per unit time. Under the first two replacement rules, the paper generates semi-Markov decision processes so that optimal policies can be obtained by the policy-iteration method. Sufficient conditions for the existence of an optimal control-limit state-dependent replacement rule are derived. For the age-dependent policy, the objective function is obtained so that the minimization can be carried out over the integers. An illustrative example is given at the end.

Suggested Citation

  • Edward P. C. Kao, 1973. "Optimal Replacement Rules when Changes of State are Semi-Markovian," Operations Research, INFORMS, vol. 21(6), pages 1231-1249, December.
    • Handle: RePEc:inm:oropre:v:21:y:1973:i:6:p:1231-1249
    DOI: 10.1287/opre.21.6.1231
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    Cited by:

    1. Panagiotidou, S. & Tagaras, G., 2012. "Optimal integrated process control and maintenance under general deterioration," Reliability Engineering and System Safety, Elsevier, vol. 104(C), pages 58-70.
    2. Ece Zeliha Demirci & Joachim Arts & Geert-Jan Van Houtum, 2022. "A restless bandit approach for capacitated condition based maintenance scheduling," DEM Discussion Paper Series 22-01, Department of Economics at the University of Luxembourg.
    3. Panagiotidou, Sofia & Tagaras, George, 2007. "Optimal preventive maintenance for equipment with two quality states and general failure time distributions," European Journal of Operational Research, Elsevier, vol. 180(1), pages 329-353, July.
    4. Ahmadi, Reza & Fouladirad, Mitra, 2017. "Maintenance planning for a deteriorating production process," Reliability Engineering and System Safety, Elsevier, vol. 159(C), pages 108-118.
    5. Yeh, Ruey Huei, 1997. "Optimal inspection and replacement policies for multi-state deteriorating systems," European Journal of Operational Research, Elsevier, vol. 96(2), pages 248-259, January.
    6. Iakovou, Eleftherios & Ip, Chi M. & Koulamas, Christos, 1996. "Optimal solutions for the machining economics problem with stochastically distributed tool lives," European Journal of Operational Research, Elsevier, vol. 92(1), pages 63-68, July.
    7. Alaa H. Elwany & Nagi Z. Gebraeel & Lisa M. Maillart, 2011. "Structured Replacement Policies for Components with Complex Degradation Processes and Dedicated Sensors," Operations Research, INFORMS, vol. 59(3), pages 684-695, June.
    8. Reza Ahmadi, 2014. "Optimal maintenance scheduling for a complex manufacturing system subject to deterioration," Annals of Operations Research, Springer, vol. 217(1), pages 1-29, June.
    9. Ahmadi, Reza & Newby, Martin, 2011. "Maintenance scheduling of a manufacturing system subject to deterioration," Reliability Engineering and System Safety, Elsevier, vol. 96(10), pages 1411-1420.
    10. Panagiotidou, Sofia & Nenes, George, 2009. "An economically designed, integrated quality and maintenance model using an adaptive Shewhart chart," Reliability Engineering and System Safety, Elsevier, vol. 94(3), pages 732-741.

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