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

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  • 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
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    References listed on IDEAS

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    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, September.
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    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.

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