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Optimal replacement rules based on different information levels

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  • Gert Heinrich
  • Uwe Jensen

Abstract

We consider the following replacement model in reliability theory. A technical system with random lifetime is replaced upon failure. Preventive replacements can be carried out before failure. The time for such a replacement depends on the observation of a random state parameter and is therefore in general a random time. Different costs for preventive and failure replacements are introduced which may depend on the age of the working system. The optimization criterion followed here to find an optimal replacement time is to minimize the total expected discounted costs. The optimal replacement policy depends on the observation of the state of the system. Results of the theory of stochastic processes are used to obtain the optimal strategy for different information levels. Several examples based on a two‐component parallel system with possibly dependent component lifetimes show how the optimal replacement policy depends on the different information levels and on the degree of dependence of the components. © 1992 John Wiley & Sons, Inc.

Suggested Citation

  • Gert Heinrich & Uwe Jensen, 1992. "Optimal replacement rules based on different information levels," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(7), pages 937-955, December.
    • Handle: RePEc:wly:navres:v:39:y:1992:i:7:p:937-955
    DOI: 10.1002/1520-6750(199212)39:73.0.CO;2-C
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    References listed on IDEAS

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    1. Ciriaco Valdez‐Flores & Richard M. Feldman, 1989. "A survey of preventive maintenance models for stochastically deteriorating single‐unit systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 36(4), pages 419-446, August.
    2. William P. Pierskalla & John A. Voelker, 1976. "A survey of maintenance models: The control and surveillance of deteriorating systems," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 23(3), pages 353-388, September.
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    Cited by:

    1. Le, Minh Duc & Tan, Cher Ming, 2013. "Optimal maintenance strategy of deteriorating system under imperfect maintenance and inspection using mixed inspectionscheduling," Reliability Engineering and System Safety, Elsevier, vol. 113(C), pages 21-29.
    2. A Barros & A Grall & C Berenguer, 2007. "Joint modelling and optimization of monitoring and maintenance performance for a two-unit parallel system," Journal of Risk and Reliability, , vol. 221(1), pages 1-11, March.
    3. Barros, A. & Bérenguer, C. & Grall, A., 2005. "On the hazard rate process for imperfectly monitored multi-unit systems," Reliability Engineering and System Safety, Elsevier, vol. 90(2), pages 169-176.
    4. R Flage & T Aven, 2011. "Optimal periodic condition inspection and replacement policy for a binary monotone system using a counting process approach," Journal of Risk and Reliability, , vol. 225(2), pages 161-168, June.

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