IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v87y2018i2d10.1007_s00186-017-0617-x.html
   My bibliography  Save this article

Component importance based on dependence measures

Author

Listed:
  • Mario Hellmich

    (Bundesamt für kerntechnische Entsorgungssicherheit (Federal Office for the Safety of Nuclear Waste Management))

Abstract

We discuss the construction of component importance measures for binary coherent reliability systems from known stochastic dependence measures by measuring the dependence between system and component failures. We treat both the time-dependent case in which the system and its components are described by binary random variables at a fixed instant as well as the continuous time case where the system and component life times are random variables. As dependence measures we discuss covariance and mutual information, the latter being based on Shannon entropy. We prove some basic properties of the resulting importance measures and obtain results on importance ordering of components.

Suggested Citation

  • Mario Hellmich, 2018. "Component importance based on dependence measures," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 87(2), pages 229-250, April.
    • Handle: RePEc:spr:mathme:v:87:y:2018:i:2:d:10.1007_s00186-017-0617-x
    DOI: 10.1007/s00186-017-0617-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00186-017-0617-x
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00186-017-0617-x?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. Marco Scarsini, 1984. "Strong measures of concordance and convergence in probability," Post-Print hal-00542387, HAL.
    2. Natvig, Bent, 1979. "A suggestion of a new measure of importance of system components," Stochastic Processes and their Applications, Elsevier, vol. 9(3), pages 319-330, December.
    3. Nader Ebrahimi & Ehsan S. Soofi & Refik Soyer, 2010. "Information Measures in Perspective," International Statistical Review, International Statistical Institute, vol. 78(3), pages 383-412, December.
    4. George Kimeldorf & Allan Sampson, 1989. "A framework for positive dependence," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 41(1), pages 31-45, March.
    5. Bent Natvig, 2011. "Measures of Component Importance in Nonrepairable and Repairable Multistate Strongly Coherent Systems," Methodology and Computing in Applied Probability, Springer, vol. 13(3), pages 523-547, September.
    6. Marco Scarsini, 1984. "On measures of concordance," Post-Print hal-00542380, HAL.
    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. Plischke, Elmar & Borgonovo, Emanuele, 2019. "Copula theory and probabilistic sensitivity analysis: Is there a connection?," European Journal of Operational Research, Elsevier, vol. 277(3), pages 1046-1059.
    2. Serkan Eryilmaz, 2013. "Component importance for linear consecutive‐ k ‐Out‐of‐ n and m ‐Consecutive‐ k ‐Out‐of‐ n systems with exchangeable components," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(4), pages 313-320, June.
    3. Edoardo Berton & Lorenzo Mercuri, 2021. "An Efficient Unified Approach for Spread Option Pricing in a Copula Market Model," Papers 2112.11968, arXiv.org, revised Feb 2023.
    4. Jiří Dvořák & Tomáš Mrkvička, 2022. "Graphical tests of independence for general distributions," Computational Statistics, Springer, vol. 37(2), pages 671-699, April.
    5. Liebscher Eckhard, 2017. "Copula-Based Dependence Measures For Piecewise Monotonicity," Dependence Modeling, De Gruyter, vol. 5(1), pages 198-220, August.
    6. Dalia Valencia & Rosa E. Lillo & Juan Romo, 2019. "A Kendall correlation coefficient between functional data," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 13(4), pages 1083-1103, December.
    7. Huseby, Arne B. & Natvig, Bent, 2013. "Discrete event simulation methods applied to advanced importance measures of repairable components in multistate network flow systems," Reliability Engineering and System Safety, Elsevier, vol. 119(C), pages 186-198.
    8. Sergio Ocampo, 2019. "A task-based theory of occupations with multidimensional heterogeneity," 2019 Meeting Papers 477, Society for Economic Dynamics.
    9. Hofert, Marius & Oldford, Wayne, 2018. "Visualizing dependence in high-dimensional data: An application to S&P 500 constituent data," Econometrics and Statistics, Elsevier, vol. 8(C), pages 161-183.
    10. Liebscher, Eckhard, 2021. "Kendall regression coefficient," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).
    11. Ferreira Helena & Ferreira Marta, 2020. "Multivariate medial correlation with applications," Dependence Modeling, De Gruyter, vol. 8(1), pages 361-372, January.
    12. Jia-Han Shih & Takeshi Emura, 2019. "Bivariate dependence measures and bivariate competing risks models under the generalized FGM copula," Statistical Papers, Springer, vol. 60(4), pages 1101-1118, August.
    13. Manuela Schreyer & Roland Paulin & Wolfgang Trutschnig, 2017. "On the exact region determined by Kendall's τ and Spearman's ρ," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(2), pages 613-633, March.
    14. Ferreira Helena & Ferreira Marta, 2020. "Multivariate medial correlation with applications," Dependence Modeling, De Gruyter, vol. 8(1), pages 361-372, January.
    15. Kochar, Subhash & Xu, Maochao, 2008. "A new dependence ordering with applications," Journal of Multivariate Analysis, Elsevier, vol. 99(9), pages 2172-2184, October.
    16. Vanderford Courtney & Sang Yongli & Dang Xin, 2020. "Two symmetric and computationally efficient Gini correlations," Dependence Modeling, De Gruyter, vol. 8(1), pages 373-395, January.
    17. Silvia Terzi & Luca Moroni, 2022. "Local Concordance and Some Applications," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 161(2), pages 457-470, June.
    18. Kamil Gala, 2015. "On the probability distribution of the present value of benefits in multiple life insurance," Collegium of Economic Analysis Annals, Warsaw School of Economics, Collegium of Economic Analysis, issue 37, pages 13-38.
    19. Machová Renáta & Korcsmáros Enikő & Marča Roland & Esseová Monika, 2022. "An International Analysis of Consumers’ Consciousness During the Covid-19 Pandemic in Slovakia and Hungary," Folia Oeconomica Stetinensia, Sciendo, vol. 22(1), pages 130-151, June.
    20. Dolati, Ali & Genest, Christian & Kochar, Subhash C., 2008. "On the dependence between the extreme order statistics in the proportional hazards model," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 777-786, May.

    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:spr:mathme:v:87:y:2018:i:2:d:10.1007_s00186-017-0617-x. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.