IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v45y1997i3p437-454.html
   My bibliography  Save this article

A unified treatment of single component replacement models

Author

Listed:
  • Hans Frenk
  • Rommert Dekker
  • Marcel Kleijn

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. Finally, some well-known replacement models are discussed, and making use of the previous results an easy derivation of their cost functions is presented. Copyright Physica-Verlag 1997

Suggested Citation

  • 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.
    • Handle: RePEc:spr:mathme:v:45:y:1997:i:3:p:437-454
    DOI: 10.1007/BF01194789
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/BF01194789
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/BF01194789?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Wang, Hongzhou, 2002. "A survey of maintenance policies of deteriorating systems," European Journal of Operational Research, Elsevier, vol. 139(3), pages 469-489, June.
    2. Dekker, Rommert, 1995. "Integrating optimisation, priority setting, planning and combining of maintenance activities," European Journal of Operational Research, Elsevier, vol. 82(2), pages 225-240, April.
    3. 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.
    4. 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.
    5. van Dijkhuizen, Gerhard C. & van Harten, Aart, 1998. "Two-stage generalized age maintenance of a queue-like production system," European Journal of Operational Research, Elsevier, vol. 108(2), pages 363-378, July.
    6. Rommert Dekker & Eric Smeitink, 1994. "Preventive maintenance at opportunities of restricted duration," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(3), pages 335-353, April.
    7. Xiang, Yisha, 2013. "Joint optimization of X¯ control chart and preventive maintenance policies: A discrete-time Markov chain approach," European Journal of Operational Research, Elsevier, vol. 229(2), pages 382-390.
    8. Vineyard, Michael & Amoako-Gyampah, Kwasi & Meredith, Jack R., 1999. "Failure rate distributions for flexible manufacturing systems: An empirical study," European Journal of Operational Research, Elsevier, vol. 116(1), pages 139-155, July.
    9. Sheu, Shey-Huei, 1998. "A generalized age and block replacement of a system subject to shocks," European Journal of Operational Research, Elsevier, vol. 108(2), pages 345-362, July.
    10. Hassin, Refael & Sarid, Anna, 2018. "Operations research applications of dichotomous search," European Journal of Operational Research, Elsevier, vol. 265(3), pages 795-812.
    11. Zheng, Junjun & Okamura, Hiroyuki & Dohi, Tadashi, 2021. "Age replacement with Markovian opportunity process," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    12. B C Giri & T Dohi, 2005. "Exact formulation of stochastic EMQ model for an unreliable production system," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(5), pages 563-575, May.
    13. David T. Abdul‐Malak & Jeffrey P. Kharoufeh & Lisa M. Maillart, 2019. "Maintaining systems with heterogeneous spare parts," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(6), pages 485-501, September.
    14. Belyi, Dmitriy & Popova, Elmira & Morton, David P. & Damien, Paul, 2017. "Bayesian failure-rate modeling and preventive maintenance optimization," European Journal of Operational Research, Elsevier, vol. 262(3), pages 1085-1093.
    15. 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.
    16. Quan, Gang & Greenwood, Garrison W. & Liu, Donglin & Hu, Sharon, 2007. "Searching for multiobjective preventive maintenance schedules: Combining preferences with evolutionary algorithms," European Journal of Operational Research, Elsevier, vol. 177(3), pages 1969-1984, March.
    17. Linderman, Kevin & McKone-Sweet, Kathleen E. & Anderson, John C., 2005. "An integrated systems approach to process control and maintenance," European Journal of Operational Research, Elsevier, vol. 164(2), pages 324-340, July.
    18. Alaswad, Suzan & Xiang, Yisha, 2017. "A review on condition-based maintenance optimization models for stochastically deteriorating system," Reliability Engineering and System Safety, Elsevier, vol. 157(C), pages 54-63.
    19. 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.
    20. Chakravarty, Amiya K. & Balakrishnan, Nagraj, 1997. "Job sequencing rules for minimizing the expected makespan in flexible machines," European Journal of Operational Research, Elsevier, vol. 96(2), pages 274-288, January.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:mathme:v:45:y:1997:i:3:p:437-454. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.