IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v181y2010i1p723-74410.1007-s10479-009-0679-0.html
   My bibliography  Save this article

Optimal age-replacement model with age-dependent type of failure and random lead time based on a cumulative repair-cost limit policy

Author

Listed:
  • Yu-Hung Chien
  • Chin-Chih Chang
  • Shey-Huei Sheu

Abstract

In this paper, we consider an age-replacement model with minimal repair based on a cumulative repair cost limit and random lead time for replacement delivery. A cumulative repair cost limit policy uses information about a system’s entire repair cost history to decide whether the system is repaired or replaced; a random lead time models delay in delivery of a replacement once it is ordered. A general cost model is developed for the average cost per unit time based on the stochastic behavior of the assumed system, reflecting the costs of both storing a spare and of system downtime. The optimal age for preventive replacement minimizing that cost rate is derived, its existence and uniqueness is shown, and structural properties are presented. Various special cases are included, and a numerical example is given for illustration. Because the framework and analysis are general, the proposed model extends several existing results. Copyright Springer Science+Business Media, LLC 2010

Suggested Citation

  • Yu-Hung Chien & Chin-Chih Chang & Shey-Huei Sheu, 2010. "Optimal age-replacement model with age-dependent type of failure and random lead time based on a cumulative repair-cost limit policy," Annals of Operations Research, Springer, vol. 181(1), pages 723-744, December.
    • Handle: RePEc:spr:annopr:v:181:y:2010:i:1:p:723-744:10.1007/s10479-009-0679-0
    DOI: 10.1007/s10479-009-0679-0
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-009-0679-0
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-009-0679-0?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 search for a different version of it.

    References listed on IDEAS

    as
    1. s.‐H. Sheu, 1999. "A general ordering policy with number‐dependentminimal repair and random lead time," Annals of Operations Research, Springer, vol. 91(0), pages 227-250, January.
    2. Richard Barlow & Larry Hunter, 1960. "Optimum Preventive Maintenance Policies," Operations Research, INFORMS, vol. 8(1), pages 90-100, February.
    3. Shey-Huei Sheu & Griffith, William S. & Toshio Nakagawa, 1995. "Extended optimal replacement model with random minimal repair costs," European Journal of Operational Research, Elsevier, vol. 85(3), pages 636-649, September.
    4. Sheu, Shey-Huei & Chien, Yu-Hung, 2004. "Optimal age-replacement policy of a system subject to shocks with random lead-time," European Journal of Operational Research, Elsevier, vol. 159(1), pages 132-144, November.
    5. Nakagawa, Toshio & Kowada, Masashi, 1983. "Analysis of a system with minimal repair and its application to replacement policy," European Journal of Operational Research, Elsevier, vol. 12(2), pages 176-182, February.
    6. Chien, Yu-Hung & Sheu, Shey-Huei & Zhang, Zhe George & Love, Ernie, 2006. "An extended optimal replacement model of systems subject to shocks," European Journal of Operational Research, Elsevier, vol. 175(1), pages 399-412, November.
    7. Frank Beichelt, 1993. "A unifying treatment of replacement policies with minimal repair," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(1), pages 51-67, February.
    8. Shey‐Huei Sheu & William S. Griffith, 1996. "Optimal number of minimal repairs before replacement of a system subject to shocks," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(3), pages 319-333, April.
    9. Philip J. Boland & Frank Proschan, 1983. "Optimum Replacement of a System Subject to Shocks," Operations Research, INFORMS, vol. 31(4), pages 697-704, August.
    10. Chien, Yu-Hung & Sheu, Shey-Huei, 2006. "Extended optimal age-replacement policy with minimal repair of a system subject to shocks," European Journal of Operational Research, Elsevier, vol. 174(1), pages 169-181, October.
    11. Philip J. Boland, 1982. "Periodic replacement when minimal repair costs vary with time," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 29(4), pages 541-546, December.
    12. Daoud Ait Kadi & Robert Cléroux, 1988. "Optimal block replacement policies with multiple choice at failure," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(1), pages 99-110, February.
    13. Philip J. Boland & Frank Proschan, 1982. "Periodic Replacement with Increasing Minimal Repair Costs at Failure," Operations Research, INFORMS, vol. 30(6), pages 1183-1189, December.
    14. R. Cléroux & S. Dubuc & C. Tilquin, 1979. "The Age Replacement Problem with Minimal Repair and Random Repair Costs," Operations Research, INFORMS, vol. 27(6), pages 1158-1167, December.
    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. Caiyun Niu & Xiaolin Liang & Bingfeng Ge & Xue Tian & Yingwu Chen, 2016. "Optimal replacement policy for a repairable system with deterioration based on a renewal-geometric process," Annals of Operations Research, Springer, vol. 244(1), pages 49-66, September.
    2. Chien, Yu-Hung & Sheu, Shey-Huei & Zhang, Zhe George, 2012. "Optimal maintenance policy for a system subject to damage in a discrete time process," Reliability Engineering and System Safety, Elsevier, vol. 103(C), pages 1-10.
    3. Xufeng Zhao & Toshio Nakagawa, 2016. "Over-time and over-level replacement policies with random working cycles," Annals of Operations Research, Springer, vol. 244(1), pages 103-116, September.
    4. Zhao, Xufeng & Qian, Cunhua & Nakagawa, Toshio, 2013. "Optimal policies for cumulative damage models with maintenance last and first," Reliability Engineering and System Safety, Elsevier, vol. 110(C), pages 50-59.
    5. Min-Tsai Lai & Huey Yan, 2016. "Optimal number of minimal repairs with cumulative repair cost limit for a two-unit system with failure rate interactions," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(2), pages 466-473, January.
    6. Yonit Barron, 2018. "Group maintenance policies for an R-out-of-N system with phase-type distribution," Annals of Operations Research, Springer, vol. 261(1), pages 79-105, February.

    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. Shey-Huei Sheu & Chin-Chih Chang & Yu-Hung Chien, 2011. "Optimal age-replacement time with minimal repair based on cumulative repair-cost limit for a system subject to shocks," Annals of Operations Research, Springer, vol. 186(1), pages 317-329, June.
    2. Sheu, Shey-Huei & Liu, Tzu-Hsin & Zhang, Zhe-George, 2019. "Extended optimal preventive replacement policies with random working cycle," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 398-415.
    3. J-A Chen & Y-H Chien, 2007. "Optimal age-replacement policy for renewing warranted products," Journal of Risk and Reliability, , vol. 221(4), pages 229-237, December.
    4. Y-H Chien & C-C Chang & S-H Sheu, 2009. "Optimal periodical time for preventive replacement based on a cumulative repair-cost limit and random lead time," Journal of Risk and Reliability, , vol. 223(4), pages 333-345, December.
    5. 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.
    6. Sheu, Shey-Huei & Tsai, Hsin-Nan & Sheu, Uan-Yu & Zhang, Zhe George, 2019. "Optimal replacement policies for a system based on a one-cycle criterion," Reliability Engineering and System Safety, Elsevier, vol. 191(C).
    7. Lim, J.H. & Qu, Jian & Zuo, Ming J., 2016. "Age replacement policy based on imperfect repair with random probability," Reliability Engineering and System Safety, Elsevier, vol. 149(C), pages 24-33.
    8. Chien, Yu-Hung & Sheu, Shey-Huei, 2006. "Extended optimal age-replacement policy with minimal repair of a system subject to shocks," European Journal of Operational Research, Elsevier, vol. 174(1), pages 169-181, October.
    9. Shey-Huei Sheu & Tzu-Hsin Liu & Wei-Teng Sheu & Yu-Hung Chien & Zhe-George Zhang, 2024. "Extended replacement policy for a system under shocks effect," Annals of Operations Research, Springer, vol. 340(1), pages 507-530, September.
    10. 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.
    11. Sheu, Shey-Huei, 1999. "Extended optimal replacement model for deteriorating systems," European Journal of Operational Research, Elsevier, vol. 112(3), pages 503-516, February.
    12. Chien, Yu-Hung & Chen, Jih-An, 2008. "Optimal spare ordering policy under a rebate warranty," European Journal of Operational Research, Elsevier, vol. 186(2), pages 708-719, April.
    13. Sheu, Shey-Huei & Chien, Yu-Hung, 2004. "Optimal age-replacement policy of a system subject to shocks with random lead-time," European Journal of Operational Research, Elsevier, vol. 159(1), pages 132-144, November.
    14. Savaş Dayanik & Ülkü Gürler, 2002. "An Adaptive Bayesian Replacement Policy with Minimal Repair," Operations Research, INFORMS, vol. 50(3), pages 552-558, June.
    15. Chien, Yu-Hung & Sheu, Shey-Huei & Zhang, Zhe George & Love, Ernie, 2006. "An extended optimal replacement model of systems subject to shocks," European Journal of Operational Research, Elsevier, vol. 175(1), pages 399-412, November.
    16. Chien, Yu-Hung, 2008. "A general age-replacement model with minimal repair under renewing free-replacement warranty," European Journal of Operational Research, Elsevier, vol. 186(3), pages 1046-1058, May.
    17. Shey-Huei Sheu & Tzu-Hsin Liu & Zhe-George Zhang & Hsin-Nan Tsai & Jung-Chih Chen, 2016. "Optimal two-threshold replacement policy in a cumulative damage model," Annals of Operations Research, Springer, vol. 244(1), pages 23-47, September.
    18. Sheu, Shey-Huei & Liu, Tzu-Hsin & Zhang, Zhe-George & Tsai, Hsin-Nan, 2018. "The generalized age maintenance policies with random working times," Reliability Engineering and System Safety, Elsevier, vol. 169(C), pages 503-514.
    19. Sheu, Shey-Huei & Chang, Chin-Chih & Zhang, Zhe George & Chien, Yu-Hung, 2012. "A note on replacement policy for a system subject to non-homogeneous pure birth shocks," European Journal of Operational Research, Elsevier, vol. 216(2), pages 503-508.
    20. SamatlI-Pa, Glay & Taner, Mehmet R., 2009. "The role of repair strategy in warranty cost minimization: An investigation via quasi-renewal processes," European Journal of Operational Research, Elsevier, vol. 197(2), pages 632-641, September.

    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:annopr:v:181:y:2010:i:1:p:723-744:10.1007/s10479-009-0679-0. 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.