IDEAS home Printed from https://ideas.repec.org/a/sae/risrel/v230y2016i1p54-66.html
   My bibliography  Save this article

Kernel-based nonparametric estimation methods for a periodic replacement problem with minimal repair

Author

Listed:
  • Yasuhiro Saito
  • Tadashi Dohi
  • Won Y Yun

Abstract

In this article, we consider nonparametric estimation methods for a periodic replacement problem with minimal repair, where the expected cumulative number of failures (minimal repairs) is unknown. To construct the confidence interval of an estimator of the optimal periodic replacement time which minimizes the long-run average cost per unit time, we apply two kernel-based bootstrap estimation methods and three replication techniques for bootstrap samples, to estimate the optimal periodic replacement time under incomplete knowledge on the failure time distribution. In simulation experiments, we compare those results with the well-known constrained nonparametric maximum likelihood estimate and some parametric models. We also conduct the field data analysis based on an actual minimal repair data and refer to an applicability of our methods.

Suggested Citation

  • Yasuhiro Saito & Tadashi Dohi & Won Y Yun, 2016. "Kernel-based nonparametric estimation methods for a periodic replacement problem with minimal repair," Journal of Risk and Reliability, , vol. 230(1), pages 54-66, February.
    • Handle: RePEc:sae:risrel:v:230:y:2016:i:1:p:54-66
    DOI: 10.1177/1748006X15601940
    as

    Download full text from publisher

    File URL: https://journals.sagepub.com/doi/10.1177/1748006X15601940
    Download Restriction: no
    File URL: https://libkey.io/10.1177/1748006X15601940?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
    ---><---

    References listed on IDEAS

    as
    1. K. Rinsaka & T. Dohi, 2007. "Estimating Age Replacement Policies From Small Sample Data," World Scientific Book Chapters, in: Tadashi Dohi & Shunji Osaki & Katsushige Sawaki (ed.), Recent Advances In Stochastic Operations Research, chapter 10, pages 145-158, World Scientific Publishing Co. Pte. Ltd..
    2. Christian Léger & Robert Cléroux, 1992. "Nonparametric Age Replacement: Bootstrap Confidence Intervals for the Optimal Cost," Operations Research, INFORMS, vol. 40(6), pages 1062-1073, December.
    3. Richard Barlow & Larry Hunter, 1960. "Optimum Preventive Maintenance Policies," Operations Research, INFORMS, vol. 8(1), pages 90-100, February.
    4. Yongtao Guan, 2007. "A Composite Likelihood Cross‐validation Approach in Selecting Bandwidth for the Estimation of the Pair Correlation Function," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 34(2), pages 336-346, June.
    5. 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.
    6. Gilardoni, Gustavo L. & Oliveira, Maristela D. de & Colosimo, Enrico A., 2013. "Nonparametric estimation and bootstrap confidence intervals for the optimal maintenance time of a repairable system," Computational Statistics & Data Analysis, Elsevier, vol. 63(C), pages 113-124.
    7. Toshio Nakagawa, 2005. "Maintenance Theory of Reliability," Springer Series in Reliability Engineering, Springer, number 978-1-84628-221-8, March.
    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. Zhao, Xufeng & Qian, Cunhua & Nakagawa, Toshio, 2017. "Comparisons of replacement policies with periodic times and repair numbers," Reliability Engineering and System Safety, Elsevier, vol. 168(C), pages 161-170.

    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. 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.
    2. Chien, Yu-Hung & Zhang, Zhe George & Yin, Xiaoling, 2019. "On optimal preventive-maintenance policy for generalized Polya process repairable products under free-repair warranty," European Journal of Operational Research, Elsevier, vol. 279(1), pages 68-78.
    3. Chien, Yu-Hung, 2019. "The optimal preventive-maintenance policy for a NHPBP repairable system under free-repair warranty," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 444-453.
    4. 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).
    5. 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.
    6. Zhang, Qin & Fang, Zhigeng & Cai, Jiajia, 2021. "Preventive replacement policies with multiple missions and maintenance triggering approaches," Reliability Engineering and System Safety, Elsevier, vol. 213(C).
    7. Somayyeh Shahraki Dehsoukhteh & Mostafa Razmkhah & Bruno Castanier, 2024. "Optimal block replacement based on expert judgement method," Journal of Risk and Reliability, , vol. 238(3), pages 591-603, June.
    8. 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).
    9. 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).
    10. 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.
    11. 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).
    12. 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).
    13. Cha, Ji Hwan & Finkelstein, Maxim, 2024. "Preventive maintenance for the constrained multi-attempt minimal repair," Reliability Engineering and System Safety, Elsevier, vol. 243(C).
    14. 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.
    15. 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.
    16. 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).
    17. 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.
    18. Sharafali, Moosa & Tarakci, Hakan & Kulkarni, Shailesh & Razack Shahul Hameed, Raja Abdul, 2019. "Optimal delivery due date for a supplier with an unreliable machine under outsourced maintenance," International Journal of Production Economics, Elsevier, vol. 208(C), pages 53-68.
    19. 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.
    20. Gilardoni, Gustavo L. & de Toledo, Maria Luiza Guerra & Freitas, Marta A. & Colosimo, Enrico A., 2016. "Dynamics of an optimal maintenance policy for imperfect repair models," European Journal of Operational Research, Elsevier, vol. 248(3), pages 1104-1112.

    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:sae:risrel:v:230:y:2016:i:1:p:54-66. 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: SAGE Publications (email available below). General contact details of provider: .

    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.