IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v95y2010i2p134-142.html
   My bibliography  Save this article

Regression analysis of the structure function for reliability evaluation of continuous-state system

Author

Listed:
  • Gámiz, M.L.
  • Martínez Miranda, M.D.

Abstract

Technical systems are designed to perform an intended task with an admissible range of efficiency. According to this idea, it is permissible that the system runs among different levels of performance, in addition to complete failure and the perfect functioning one. As a consequence, reliability theory has evolved from binary-state systems to the most general case of continuous-state system, in which the state of the system changes over time through some interval on the real number line. In this context, obtaining an expression for the structure function becomes difficult, compared to the discrete case, with difficulty increasing as the number of components of the system increases. In this work, we propose a method to build a structure function for a continuum system by using multivariate nonparametric regression techniques, in which certain analytical restrictions on the variable of interest must be taken into account. Once the structure function is obtained, some reliability indices of the system are estimated. We illustrate our method via several numerical examples.

Suggested Citation

  • Gámiz, M.L. & Martínez Miranda, M.D., 2010. "Regression analysis of the structure function for reliability evaluation of continuous-state system," Reliability Engineering and System Safety, Elsevier, vol. 95(2), pages 134-142.
    • Handle: RePEc:eee:reensy:v:95:y:2010:i:2:p:134-142
    DOI: 10.1016/j.ress.2009.09.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0951832009002245
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ress.2009.09.004?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Gonzalez Manteiga, W. & Martinez Miranda, M. D. & Perez Gonzalez, A., 2004. "The choice of smoothing parameter in nonparametric regression through Wild Bootstrap," Computational Statistics & Data Analysis, Elsevier, vol. 47(3), pages 487-515, October.
    2. Gregory Levitin, 2005. "The Universal Generating Function in Reliability Analysis and Optimization," Springer Series in Reliability Engineering, Springer, number 978-1-84628-245-4, April.
    3. Chen, Song Xi, 1999. "Beta kernel estimators for density functions," Computational Statistics & Data Analysis, Elsevier, vol. 31(2), pages 131-145, August.
    Full references (including those not matched with items on IDEAS)

    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. Hirukawa, Masayuki, 2010. "Nonparametric multiplicative bias correction for kernel-type density estimation on the unit interval," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 473-495, February.
    2. Ouimet, Frédéric & Tolosana-Delgado, Raimon, 2022. "Asymptotic properties of Dirichlet kernel density estimators," Journal of Multivariate Analysis, Elsevier, vol. 187(C).
    3. Bouezmarni, Taoufik & Van Bellegem, Sébastien, 2009. "Nonparametric Beta Kernel Estimator for Long Memory Time Series," IDEI Working Papers 633, Institut d'Économie Industrielle (IDEI), Toulouse.
    4. Hagmann, M. & Scaillet, O., 2007. "Local multiplicative bias correction for asymmetric kernel density estimators," Journal of Econometrics, Elsevier, vol. 141(1), pages 213-249, November.
    5. Fernandes, Marcelo & Grammig, Joachim, 2005. "Nonparametric specification tests for conditional duration models," Journal of Econometrics, Elsevier, vol. 127(1), pages 35-68, July.
    6. Li, Chun-yang & Chen, Xun & Yi, Xiao-shan & Tao, Jun-yong, 2010. "Heterogeneous redundancy optimization for multi-state series–parallel systems subject to common cause failures," Reliability Engineering and System Safety, Elsevier, vol. 95(3), pages 202-207.
    7. Zhao, Xian & He, Zongda & Wu, Yaguang & Qiu, Qingan, 2022. "Joint optimization of condition-based performance control and maintenance policies for mission-critical systems," Reliability Engineering and System Safety, Elsevier, vol. 226(C).
    8. Nikolay Gospodinov & Masayuki Hirukawa, 2008. "Time Series Nonparametric Regression Using Asymmetric Kernels with an Application to Estimation of Scalar Diffusion Processes," CIRJE F-Series CIRJE-F-573, CIRJE, Faculty of Economics, University of Tokyo.
    9. Tian, Tianzi & Yang, Jun & Li, Lei & Wang, Ning, 2023. "Reliability assessment of performance-based balanced systems with rebalancing mechanisms," Reliability Engineering and System Safety, Elsevier, vol. 233(C).
    10. Salvatore D. Tomarchio & Antonio Punzo, 2019. "Modelling the loss given default distribution via a family of zero‐and‐one inflated mixture models," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 182(4), pages 1247-1266, October.
    11. Chen, Yiming & Liu, Yu & Jiang, Tao, 2021. "Optimal maintenance strategy for multi-state systems with single maintenance capacity and arbitrarily distributed maintenance time," Reliability Engineering and System Safety, Elsevier, vol. 211(C).
    12. Hausken, Kjell & Levitin, Gregory, 2009. "Minmax defense strategy for complex multi-state systems," Reliability Engineering and System Safety, Elsevier, vol. 94(2), pages 577-587.
    13. Grammig, Joachim G. & Peter, Franziska J., 2008. "International price discovery in the presence of market microstructure effects," CFR Working Papers 08-10, University of Cologne, Centre for Financial Research (CFR).
    14. Yeh, Wei-Chang & Bae, Changseok & Huang, Chia-Ling, 2015. "A new cut-based algorithm for the multi-state flow network reliability problem," Reliability Engineering and System Safety, Elsevier, vol. 136(C), pages 1-7.
    15. Li, Yan-Fu & Zio, Enrico, 2012. "A multi-state model for the reliability assessment of a distributed generation system via universal generating function," Reliability Engineering and System Safety, Elsevier, vol. 106(C), pages 28-36.
    16. Hindolo George-Williams & Geng Feng & Frank PA Coolen & Michael Beer & Edoardo Patelli, 2019. "Extending the survival signature paradigm to complex systems with non-repairable dependent failures," Journal of Risk and Reliability, , vol. 233(4), pages 505-519, August.
    17. Nourelfath, Mustapha & Ait-Kadi, Daoud, 2007. "Optimization of series–parallel multi-state systems under maintenance policies," Reliability Engineering and System Safety, Elsevier, vol. 92(12), pages 1620-1626.
    18. Song Li & Mervyn J. Silvapulle & Param Silvapulle & Xibin Zhang, 2015. "Bayesian Approaches to Nonparametric Estimation of Densities on the Unit Interval," Econometric Reviews, Taylor & Francis Journals, vol. 34(3), pages 394-412, March.
    19. Bigatti, A.M. & Pascual-Ortigosa, P. & Sáenz-de-Cabezón, E., 2021. "A C++ class for multi-state algebraic reliability computations," Reliability Engineering and System Safety, Elsevier, vol. 213(C).
    20. Levitin, Gregory & Xing, Liudong & Dai, Yuanshun, 2024. "Optimal system loading and aborting in additive multi-attempt missions," Reliability Engineering and System Safety, Elsevier, vol. 251(C).

    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:reensy:v:95:y:2010:i:2:p:134-142. 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: https://www.journals.elsevier.com/reliability-engineering-and-system-safety .

    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.