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Nonparametric estimation and bootstrap confidence intervals for the optimal maintenance time of a repairable system

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  • Gilardoni, Gustavo L.
  • Oliveira, Maristela D. de
  • Colosimo, Enrico A.

Abstract

Consider a repairable system operating under a maintenance strategy that calls for complete preventive repair actions at pre-scheduled times and minimal repair actions whenever a failure occurs. Under minimal repair, the failures are assumed to follow a nonhomogeneous Poisson process with an increasing intensity function. This paper departs from the usual power-law-process parametric approach by using the constrained nonparametric maximum likelihood estimate of the intensity function to estimate the optimum preventive maintenance policy. Several strategies to bootstrap the failure times and construct confidence intervals for the optimal maintenance periodicity are presented and discussed. The methodology is applied to a real data set concerning the failure histories of a set of power transformers.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:63:y:2013:i:c:p:113-124
    DOI: 10.1016/j.csda.2013.02.006
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    References listed on IDEAS

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    1. Richard Barlow & Larry Hunter, 1960. "Optimum Preventive Maintenance Policies," Operations Research, INFORMS, vol. 8(1), pages 90-100, February.
    2. C. A. Field & A. H. Welsh, 2007. "Bootstrapping clustered data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(3), pages 369-390, June.
    3. Yu, Jun-Wu & Tian, Guo-Liang & Tang, Man-Lai, 2008. "Statistical inference and prediction for the Weibull process with incomplete observations," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1587-1603, January.
    4. Chin‐Tsang Chiang & Mei‐Cheng Wang & Chiung‐Yu Huang, 2005. "Kernel Estimation of Rate Function for Recurrent Event Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(1), pages 77-91, March.
    5. Yu, Jun-Wu & Tian, Guo-Liang & Tang, Man-Lai, 2007. "Predictive analyses for nonhomogeneous Poisson processes with power law using Bayesian approach," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4254-4268, May.
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    Cited by:

    1. Doyen, L., 2014. "Semi-parametric estimation of Brown–Proschan preventive maintenance effects and intrinsic wear-out," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 206-222.
    2. 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.
    3. Patawa, Rohit & Pundir, Pramendra Singh, 2023. "Inferential study of single unit repairable system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 206(C), pages 503-516.
    4. 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.

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