IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v63y2013icp113-124.html

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947313000509
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2013.02.006?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

    for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    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. 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.
    5. Richard Barlow & Larry Hunter, 1960. "Optimum Preventive Maintenance Policies," Operations Research, INFORMS, vol. 8(1), pages 90-100, 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. 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. 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.
    4. 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.

    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. Tarakci, Hakan & Tang, Kwei & Teyarachakul, Sunantha, 2009. "Learning effects on maintenance outsourcing," European Journal of Operational Research, Elsevier, vol. 192(1), pages 138-150, January.
    2. 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).
    3. Won Young Yun & Alfonsus Julanto Endharta, 2016. "A preventive replacement policy based on system critical condition," Journal of Risk and Reliability, , vol. 230(1), pages 93-100, February.
    4. Mamabolo R. M. & Beichelt F. E., 2004. "Maintenance Policies with Minimal Repair," Stochastics and Quality Control, De Gruyter, vol. 19(2), pages 143-166, January.
    5. Orth, Walter, 2010. "The predictive accuracy of credit ratings: Measurement and statistical inference," MPRA Paper 30148, University Library of Munich, Germany, revised 16 Feb 2011.
    6. Wen Shi & Xi Chen & Jennifer Shang, 2019. "An Efficient Morris Method-Based Framework for Simulation Factor Screening," INFORMS Journal on Computing, INFORMS, vol. 31(4), pages 745-770, October.
    7. Caiyun Niu & Xiaolin Liang & Bingfeng Ge & Xue Tian & Yingwu Chen, 2016. "Optimal replacement policy for a repairable system with deterioration based on a renewal-geometric process," Annals of Operations Research, Springer, vol. 244(1), pages 49-66, September.
    8. Deprez, Laurens & Antonio, Katrien & Boute, Robert, 2021. "Pricing service maintenance contracts using predictive analytics," European Journal of Operational Research, Elsevier, vol. 290(2), pages 530-545.
    9. Toledo, Maria Luíza Guerra de & Freitas, Marta A. & Colosimo, Enrico A. & Gilardoni, Gustavo L., 2015. "ARA and ARI imperfect repair models: Estimation, goodness-of-fit and reliability prediction," Reliability Engineering and System Safety, Elsevier, vol. 140(C), pages 107-115.
    10. David Roodman & James G. MacKinnon & Morten Ørregaard Nielsen & Matthew D. Webb, 2019. "Fast and wild: Bootstrap inference in Stata using boottest," Stata Journal, StataCorp LLC, vol. 19(1), pages 4-60, March.
    11. Kim, Michael Jong & Jiang, Rui & Makis, Viliam & Lee, Chi-Guhn, 2011. "Optimal Bayesian fault prediction scheme for a partially observable system subject to random failure," European Journal of Operational Research, Elsevier, vol. 214(2), pages 331-339, October.
    12. Sheu, Shey-Huei & Chien, Yu-Hung, 2004. "Optimal age-replacement policy of a system subject to shocks with random lead-time," European Journal of Operational Research, Elsevier, vol. 159(1), pages 132-144, November.
    13. Mathieu Bunel, 2012. "Evaluer un dispositif sectoriel d'aide à l'emploi : L'exemple des hôtels cafés restaurants de 2004 à 2009," Working Papers halshs-00736693, HAL.
    14. T F Lipi & J-H Lim & M J Zuo & W Wang, 2012. "A condition- and age-based replacement model using delay time modelling," Journal of Risk and Reliability, , vol. 226(2), pages 221-233, April.
    15. 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).
    16. Guo R. & Ascher H. & Love E., 2001. "Towards Practical and Synthetical Modelling of Repairable Systems," Stochastics and Quality Control, De Gruyter, vol. 16(1), pages 147-182, January.
    17. van Staden, Heletjé E. & Deprez, Laurens & Boute, Robert N., 2022. "A dynamic “predict, then optimize” preventive maintenance approach using operational intervention data," European Journal of Operational Research, Elsevier, vol. 302(3), pages 1079-1096.
    18. Chattopadhyay, Gopinath & Rahman, Anisur, 2008. "Development of lifetime warranty policies and models for estimating costs," Reliability Engineering and System Safety, Elsevier, vol. 93(4), pages 522-529.
    19. Aghezzaf, E.H. & Jamali, M.A. & Ait-Kadi, D., 2007. "An integrated production and preventive maintenance planning model," European Journal of Operational Research, Elsevier, vol. 181(2), pages 679-685, September.
    20. Biswas, Atanu & Sarkar, Jyotirmoy, 2000. "Availability of a system maintained through several imperfect repairs before a replacement or a perfect repair," Statistics & Probability Letters, Elsevier, vol. 50(2), pages 105-114, November.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:csdana:v:63:y:2013:i:c:p:113-124. 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/csda .

    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.