IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v295y2021i2p699-704.html
   My bibliography  Save this article

Revisiting discrete time age replacement policy for phase-type lifetime distributions

Author

Listed:
  • Eryilmaz, Serkan

Abstract

For a system (or unit) whose lifetime is measured by the number cycles, according to the discrete time age replacement policy, it is replaced preventively after n cycles or correctively at failure, whichever occurs first. In this paper, discrete time age replacement policy is revisited when the lifetime of the system is modeled by a discrete phase-type distribution. In particular, the necessary conditions for the unique and finite replacement cycle which minimizes the expected cost per unit of time are obtained. The necessary conditions are mainly based on the behavior of the hazard rate. The results are illustrated for some special discrete phase-type lifetime distributions. Computational results are also presented for the optimal replacement cycle under specific real life setups.

Suggested Citation

  • Eryilmaz, Serkan, 2021. "Revisiting discrete time age replacement policy for phase-type lifetime distributions," European Journal of Operational Research, Elsevier, vol. 295(2), pages 699-704.
  • Handle: RePEc:eee:ejores:v:295:y:2021:i:2:p:699-704
    DOI: 10.1016/j.ejor.2021.03.007
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221721001971
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.ejor.2021.03.007?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. Markos V. Koutras & Serkan Eryilmaz, 2017. "Compound Geometric Distribution of Order k," Methodology and Computing in Applied Probability, Springer, vol. 19(2), pages 377-393, June.
    2. 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.
    3. Fouladirad, Mitra & Paroissin, Christian & Grall, Antoine, 2018. "Sensitivity of optimal replacement policies to lifetime parameter estimates," European Journal of Operational Research, Elsevier, vol. 266(3), pages 963-975.
    4. Nakagawa, Toshio, 1984. "A summary of discrete replacement policies," European Journal of Operational Research, Elsevier, vol. 17(3), pages 382-392, September.
    5. Navarro, Jorge & Arriaza, Antonio & Suárez-Llorens, Alfonso, 2019. "Minimal repair of failed components in coherent systems," European Journal of Operational Research, Elsevier, vol. 279(3), pages 951-964.
    6. Zhao, Xufeng & Mizutani, Satoshi & Nakagawa, Toshio, 2015. "Which is better for replacement policies with continuous or discrete scheduled times?," European Journal of Operational Research, Elsevier, vol. 242(2), pages 477-486.
    7. Zhao, Xufeng & Al-Khalifa, Khalifa N. & Magid Hamouda, Abdel & Nakagawa, Toshio, 2017. "Age replacement models: A summary with new perspectives and methods," Reliability Engineering and System Safety, Elsevier, vol. 161(C), pages 95-105.
    8. Levitin, Gregory & Finkelstein, Maxim & Dai, Yuanshun, 2018. "Heterogeneous standby systems with shocks-driven preventive replacements," European Journal of Operational Research, Elsevier, vol. 266(3), pages 1189-1197.
    9. Safaei, Fatemeh & Châtelet, Eric & Ahmadi, Jafar, 2020. "Optimal age replacement policy for parallel and series systems with dependent components," Reliability Engineering and System Safety, Elsevier, vol. 197(C).
    10. Eisele, Karl-Theodor, 2006. "Recursions for compound phase distributions," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 149-156, February.
    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. Jing Wu & Cunhua Qian & Tadashi Dohi, 2024. "A Net Present Value Analysis of Opportunity-Based Age Replacement Models in Discrete Time," Mathematics, MDPI, vol. 12(10), pages 1-23, May.
    2. Eryilmaz, Serkan & Yalcin, Femin, 2022. "The number of failed components upon system failure when the lifetimes are discretely distributed," Reliability Engineering and System Safety, Elsevier, vol. 225(C).
    3. Wu, Jing & Qian, Cunhua & Dohi, Tadashi, 2024. "Optimal opportunity-based age replacement policies in discrete time," Reliability Engineering and System Safety, Elsevier, vol. 241(C).
    4. Serkan Eryilmaz & Fatih Tank, 2023. "Optimal age replacement policy for discrete time parallel systems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(3), pages 475-490, 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. Torrado, Nuria, 2022. "Optimal component-type allocation and replacement time policies for parallel systems having multi-types dependent components," Reliability Engineering and System Safety, Elsevier, vol. 224(C).
    2. Zheng, Junjun & Okamura, Hiroyuki & Dohi, Tadashi, 2021. "Age replacement with Markovian opportunity process," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    3. Kowal, Karol, 2022. "Lifetime reliability and availability simulation for the electrical system of HTTR coupled to the electricity-hydrogen cogeneration plant," Reliability Engineering and System Safety, Elsevier, vol. 223(C).
    4. Hashemi, M. & Asadi, M. & Tavangar, M., 2022. "Optimal maintenance strategies for coherent systems: A warranty dependent approach," Reliability Engineering and System Safety, Elsevier, vol. 217(C).
    5. Levitin, Gregory & Finkelstein, Maxim & Dai, Yuanshun, 2020. "Optimal preventive replacement policy for homogeneous cold standby systems with reusable elements," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    6. Serkan Eryilmaz & Fatih Tank, 2023. "Optimal age replacement policy for discrete time parallel systems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(3), pages 475-490, October.
    7. Murat Ozkut, 2022. "Comparison of the replacement policy in k-out-of-n systems having dependent components," Journal of Risk and Reliability, , vol. 236(1), pages 125-137, February.
    8. Chien, Yu-Hung, 2012. "The effects of a free-repair warranty on the discrete-time periodic replacement policy," International Journal of Production Economics, Elsevier, vol. 135(2), pages 832-839.
    9. Safaei, Fatemeh & Ahmadi, Jafar & Taghipour, Sharareh, 2022. "A maintenance policy for a k-out-of-n system under enhancing the system’s operating time and safety constraints, and selling the second-hand components," Reliability Engineering and System Safety, Elsevier, vol. 218(PA).
    10. Eryilmaz, Serkan, 2020. "Age-based preventive maintenance for coherent systems with applications to consecutive-k-out-of-n and related systems," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    11. Vasileios M. Koutras & Markos V. Koutras & Spiros D. Dafnis, 2022. "A Family of Induced Distributions," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1833-1848, September.
    12. Levitin, Gregory & Finkelstein, Maxim & Dai, Yuanshun, 2021. "Optimization of cyclic preventive replacement in homogeneous warm-standby system with reusable elements exposed to shocks," Reliability Engineering and System Safety, Elsevier, vol. 207(C).
    13. Tavangar, Mahdi & Hashemi, Marzieh, 2022. "Reliability and maintenance analysis of coherent systems subject to aging and environmental shocks," Reliability Engineering and System Safety, Elsevier, vol. 218(PB).
    14. Félix Belzunce & Carolina Martínez-Riquelme & José A. Mercader & José M. Ruiz, 2021. "Comparisons of policies based on relevation and replacement by a new one unit in reliability," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 211-227, March.
    15. de Jonge, Bram & Scarf, Philip A., 2020. "A review on maintenance optimization," European Journal of Operational Research, Elsevier, vol. 285(3), pages 805-824.
    16. Vasileios M. Koutras & Markos V. Koutras, 2020. "Exact Distribution of Random Order Statistics and Applications in Risk Management," Methodology and Computing in Applied Probability, Springer, vol. 22(4), pages 1539-1558, December.
    17. Koutras, Vasileios M. & Koutras, Markos V. & Yalcin, Femin, 2016. "A simple compound scan statistic useful for modeling insurance and risk management problems," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 202-209.
    18. Jing Wu & Cunhua Qian & Tadashi Dohi, 2024. "A Net Present Value Analysis of Opportunity-Based Age Replacement Models in Discrete Time," Mathematics, MDPI, vol. 12(10), pages 1-23, May.
    19. Eisele, Karl-Theodor, 2008. "Recursions for multivariate compound phase variables," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 65-72, February.
    20. Navarro, Jorge & Fernández-Martínez, Pedro, 2021. "Redundancy in systems with heterogeneous dependent components," European Journal of Operational Research, Elsevier, vol. 290(2), pages 766-778.

    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:eee:ejores:v:295:y:2021:i:2:p:699-704. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.