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A unified treatment of single component replacement models

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  • Frenk, J.B.G.
  • Dekker, R.
  • Kleijn, M.J.

Abstract

In this paper we discuss a general framework for single component replacement models. This framework is based on the regenerative structure of these models and by using results from renewal theory a unified presentation of the discounted and average finite and infinite horizon cost models is given. Moreover, we present sufficient conditions for the numerator of the cost function to have a vanishing singular part. Finally, some well-known replacement models are discussed, and making use of the previous results an easy derivation of their cost functions is presented.

Suggested Citation

  • Frenk, J.B.G. & Dekker, R. & Kleijn, M.J., 1996. "A unified treatment of single component replacement models," Econometric Institute Research Papers EI 9602-/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    • Handle: RePEc:ems:eureir:1370
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    References listed on IDEAS

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    1. John J. McCall, 1965. "Maintenance Policies for Stochastically Failing Equipment: A Survey," Management Science, INFORMS, vol. 11(5), pages 493-524, March.
    2. H. W. Block & W. S. Borges & T. H. Savits, 1988. "A general age replacement model with minimal repair," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(5), pages 365-372, October.
    3. Hans Frenk & Rommert Dekker & Marcel Kleijn, 1997. "A unified treatment of single component replacement models," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 45(3), pages 437-454, October.
    4. Dekker, Rommert & Smeitink, Eric, 1991. "Opportunity-based block replacement," European Journal of Operational Research, Elsevier, vol. 53(1), pages 46-63, July.
    5. Berg, Menachem P., 1995. "The marginal cost analysis and its application to repair and replacement policies," European Journal of Operational Research, Elsevier, vol. 82(2), pages 214-224, April.
    6. Zijlstra, Mynt, 1981. "Renewal replacement policies for one unit systems," European Journal of Operational Research, Elsevier, vol. 8(3), pages 289-293, November.
    7. B. D. Sivazlian, 1973. "On a Discounted Replacement Problem with Arbitrary Repair Time Distribution," Management Science, INFORMS, vol. 19(11), pages 1301-1309, July.
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    Cited by:

    1. J. B. G. Frenk & R. Dekker & M. J. Kleijn, 1997. "On the Marginal Cost Approach in Maintenance," Journal of Optimization Theory and Applications, Springer, vol. 94(3), pages 771-781, September.
    2. Wang, Hongzhou, 2002. "A survey of maintenance policies of deteriorating systems," European Journal of Operational Research, Elsevier, vol. 139(3), pages 469-489, June.
    3. Hans Frenk & Rommert Dekker & Marcel Kleijn, 1997. "A unified treatment of single component replacement models," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 45(3), pages 437-454, October.

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