IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i11p1833-d824913.html
   My bibliography  Save this article

A Preventive Replacement Policy for a System Subject to Bivariate Generalized Polya Failure Process

Author

Listed:
  • Hyunju Lee

    (Department of Statistics, Hankuk University of Foreign Studies, Yongin 17035, Korea)

  • Ji Hwan Cha

    (Department of Statistics, Ewha Womans University, Seoul 03760, Korea)

  • Maxim Finkelstein

    (Department of Mathematical Statistics, University of the Free State, Bloemfontein 9300, South Africa
    Department of Management Science, University of Strathclyde, Glasgow G1 1XQ, UK)

Abstract

Numerous studies on preventive maintenance of minimally repaired systems with statistically independent components have been reported in reliability literature. However, in practice, the repair can be worse-than-minimal and the components of a system can be statistically dependent. The existing literature does not cover this important in-practice setting. Therefore, our paper is the first to deal with these issues by modeling dependence in the bivariate set up when a system consists of two dependent parts. We employ the bivariate generalized Polya process to model the corresponding failure and repair process. Relevant stochastic properties of this process have been obtained in order to propose and further discuss the new optimal bivariate preventive maintenance policy with two decision parameters: age and operational history. Moreover, introducing these two parameters in the considered context is also a new feature of the study. Under the proposed policy, the long-run average cost rate is derived and the optimal replacement policies are investigated. Detailed numerical examples illustrate our findings and show the potential efficiency of the obtained results in practice.

Suggested Citation

  • Hyunju Lee & Ji Hwan Cha & Maxim Finkelstein, 2022. "A Preventive Replacement Policy for a System Subject to Bivariate Generalized Polya Failure Process," Mathematics, MDPI, vol. 10(11), pages 1-15, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:11:p:1833-:d:824913
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/11/1833/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/11/1833/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Bowsher, Clive G., 2007. "Modelling security market events in continuous time: Intensity based, multivariate point process models," Journal of Econometrics, Elsevier, vol. 141(2), pages 876-912, December.
    2. Richard Barlow & Larry Hunter, 1960. "Optimum Preventive Maintenance Policies," Operations Research, INFORMS, vol. 8(1), pages 90-100, February.
    3. Hongzhou Wang & Hoang Pham, 2006. "Reliability and Optimal Maintenance," Springer Series in Reliability Engineering, Springer, number 978-1-84628-325-3, December.
    4. 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.
    5. Hyunju Lee & Ji Hwan Cha, 2019. "A bivariate optimal replacement policy for a system subject to a generalized failure and repair process," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 35(3), pages 637-650, May.
    6. Partrat, Christian, 1994. "Compound model for two dependent kinds of claim," Insurance: Mathematics and Economics, Elsevier, vol. 15(2-3), pages 219-231, December.
    7. Toshio Nakagawa, 2005. "Maintenance Theory of Reliability," Springer Series in Reliability Engineering, Springer, number 978-1-84628-221-8, 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. Francisco Germán Badía & María D. Berrade, 2023. "Special Issue “Probability Theory and Stochastic Modeling with Applications”," Mathematics, MDPI, vol. 11(14), pages 1-3, July.

    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. Hashemi, M. & Asadi, M. & Zarezadeh, S., 2020. "Optimal maintenance policies for coherent systems with multi-type components," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
    2. Finkelstein, Maxim & Cha, Ji Hwan & Langston, Amy, 2023. "Improving classical optimal age-replacement policies for degrading items," Reliability Engineering and System Safety, Elsevier, vol. 236(C).
    3. Ji Hwan Cha & Maxim Finkelstein, 2020. "On optimal life extension for degrading systems," Journal of Risk and Reliability, , vol. 234(3), pages 487-495, June.
    4. 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.
    5. Finkelstein, Maxim & Cha, Ji Hwan & Bedford, Tim, 2023. "Optimal preventive maintenance strategy for populations of systems that generate outputs," Reliability Engineering and System Safety, Elsevier, vol. 237(C).
    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. Asadi, Majid, 2023. "On a parametric model for the mean number of system repairs with applications," Reliability Engineering and System Safety, Elsevier, vol. 234(C).
    8. Ji Hwan Cha & Maxim Finkelstein & Gregory Levitin, 2022. "Replacement Policy for Heterogeneous Items Subject to Gamma Degradation Processes," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1323-1340, September.
    9. Maxim Finkelstein & Gregory Levitin & Oleg A Stepanov, 2019. "On operation termination for degrading systems with two types of failures," Journal of Risk and Reliability, , vol. 233(3), pages 419-426, June.
    10. Maxim Finkelstein & Ji Hwan Cha & Amy Langston, 2023. "Termination versus operation extension for degrading systems," Journal of Risk and Reliability, , vol. 237(6), pages 1175-1185, December.
    11. Cha, Ji Hwan & Finkelstein, Maxim & Levitin, Gregory, 2021. "Optimal warranty policy with inspection for heterogeneous, stochastically degrading items," European Journal of Operational Research, Elsevier, vol. 289(3), pages 1142-1152.
    12. Cha, Ji Hwan & Finkelstein, Maxim & Levitin, Gregory, 2018. "Bivariate preventive maintenance of systems with lifetimes dependent on a random shock process," European Journal of Operational Research, Elsevier, vol. 266(1), pages 122-134.
    13. Miaomiao Yu & Yinghui Tang, 2017. "Optimal replacement policy based on maximum repair time for a random shock and wear model," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 80-94, April.
    14. Cha, Ji Hwan & Finkelstein, Maxim & Levitin, Gregory, 2017. "On preventive maintenance of systems with lifetimes dependent on a random shock process," Reliability Engineering and System Safety, Elsevier, vol. 168(C), pages 90-97.
    15. Hamdan, K. & Tavangar, M. & Asadi, M., 2021. "Optimal preventive maintenance for repairable weighted k-out-of-n systems," Reliability Engineering and System Safety, Elsevier, vol. 205(C).
    16. 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.
    17. Sheu, Shey-Huei, 1999. "Extended optimal replacement model for deteriorating systems," European Journal of Operational Research, Elsevier, vol. 112(3), pages 503-516, February.
    18. Young Yun, Won & Nakagawa, Toshio, 2010. "Replacement and inspection policies for products with random life cycle," Reliability Engineering and System Safety, Elsevier, vol. 95(3), pages 161-165.
    19. Zhou, Xiaojun & Xi, Lifeng & Lee, Jay, 2007. "Reliability-centered predictive maintenance scheduling for a continuously monitored system subject to degradation," Reliability Engineering and System Safety, Elsevier, vol. 92(4), pages 530-534.
    20. Badía, F.G. & Berrade, M.D. & Cha, Ji Hwan & Lee, Hyunju, 2018. "Optimal replacement policy under a general failure and repair model: Minimal versus worse than old repair," Reliability Engineering and System Safety, Elsevier, vol. 180(C), pages 362-372.

    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:gam:jmathe:v:10:y:2022:i:11:p:1833-:d:824913. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.