IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v59y2012i7p487-496.html
   My bibliography  Save this article

Parametric inference for component distributions from lifetimes of systems with dependent components

Author

Listed:
  • Jorge Navarro
  • Hon Keung Tony Ng
  • Narayanaswamy Balakrishnan

Abstract

In system reliability analysis, for an n ‐component system, the estimation of the performance of the components in the system is not straightforward in practice, especially when the components are dependent. Here, by assuming the n components in the system to be identically distributed with a common distribution belonging to a scale‐family and the dependence structure between the components being known, we discuss the estimation of the lifetime distributions of the components in the system based on the lifetimes of systems with the same structure. We develop a general framework for inference on the scale parameter of the component lifetime distribution. Specifically, the method of moments estimator (MME) and the maximum likelihood estimator (MLE) are derived for the scale parameter, and the conditions for the existence of the MLE are also discussed. The asymptotic confidence intervals for the scale parameter are also developed based on the MME and the MLE. General simulation procedures for the system lifetime under this model are described. Finally, some examples of two‐ and three‐component systems are presented to illustrate all the inferential procedures developed here. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012

Suggested Citation

  • Jorge Navarro & Hon Keung Tony Ng & Narayanaswamy Balakrishnan, 2012. "Parametric inference for component distributions from lifetimes of systems with dependent components," Naval Research Logistics (NRL), John Wiley & Sons, vol. 59(7), pages 487-496, October.
    • Handle: RePEc:wly:navres:v:59:y:2012:i:7:p:487-496
    DOI: 10.1002/nav.21502
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/nav.21502
    Download Restriction: no
    File URL: https://libkey.io/10.1002/nav.21502?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
    ---><---

    References listed on IDEAS

    as
    1. Narayanaswamy Balakrishnan & Hon Ng & Jorge Navarro, 2011. "Exact nonparametric inference for component lifetime distribution based on lifetime data from systems with known signatures," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(3), pages 741-752.
    2. Debasis Bhattacharya & Francisco J. Samaniego, 2010. "Estimating component characteristics from system failure‐time data," Naval Research Logistics (NRL), John Wiley & Sons, vol. 57(4), pages 380-389, June.
    3. Manuel Franco & M. Ruiz & José Ruiz, 2003. "A note on closure of the ILR and DLR classes under formation of coherent systems," Statistical Papers, Springer, vol. 44(2), pages 279-288, April.
    4. Hon Ng & Jorge Navarro & Narayanaswamy Balakrishnan, 2012. "Parametric inference from system lifetime data under a proportional hazard rate model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(3), pages 367-388, April.
    5. Christian Genest & Johanna Nešlehová & Johanna Ziegel, 2011. "Inference in multivariate Archimedean copula models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(2), pages 223-256, August.
    6. Belzunce, Félix & Ruiz, José M. & Ruiz, M. Carmen, 2002. "On preservation of some shifted and proportional orders by systems," Statistics & Probability Letters, Elsevier, vol. 60(2), pages 141-154, November.
    7. Christian Genest & Johanna Nešlehová & Johanna Ziegel, 2011. "Rejoinder on: Inference in multivariate Archimedean copula models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(2), pages 290-292, August.
    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. Erhard Cramer & Jorge Navarro, 2015. "Progressive Type‐II censoring and coherent systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(6), pages 512-530, September.
    2. Anna Dembińska & Krzysztof Jasiński, 2021. "Maximum likelihood estimators based on discrete component lifetimes of a k-out-of-n system," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(2), pages 407-428, June.
    3. Jian Zhang & Hon Keung Tony Ng & Narayanaswamy Balakrishnan, 2015. "Tests for homogeneity of distributions of component lifetimes from system lifetime data with known system signatures," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(7), pages 550-563, October.
    4. Louis J. M. Aslett & Frank P. A. Coolen & Simon P. Wilson, 2015. "Bayesian Inference for Reliability of Systems and Networks Using the Survival Signature," Risk Analysis, John Wiley & Sons, vol. 35(9), pages 1640-1651, September.
    5. Jingjing Qu & Hon Keung Tony Ng & Chul Moon, 2024. "Empirical likelihood ratio tests for homogeneity of component lifetime distributions based on system lifetime data," Computational Statistics, Springer, vol. 39(6), pages 3007-3029, September.

    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. Zhu, Xiaojun & Balakrishnan, N., 2023. "Non-parametric inference based on reliability life-test of non-identical coherent systems with application to warranty time," Reliability Engineering and System Safety, Elsevier, vol. 232(C).
    2. Jingjing Qu & Hon Keung Tony Ng & Chul Moon, 2024. "Empirical likelihood ratio tests for homogeneity of component lifetime distributions based on system lifetime data," Computational Statistics, Springer, vol. 39(6), pages 3007-3029, September.
    3. Jian Zhang & Hon Keung Tony Ng & Narayanaswamy Balakrishnan, 2015. "Tests for homogeneity of distributions of component lifetimes from system lifetime data with known system signatures," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(7), pages 550-563, October.
    4. Elena Di Bernardino & Didier Rullière, 2016. "A note on upper-patched generators for Archimedean copulas," Working Papers hal-01347869, HAL.
    5. Jia, Xujie & Shen, Jingyuan & Xu, Fanqi & Ma, Ruihong & Song, Xueying, 2019. "Modular decomposition signature for systems with sequential failure effect," Reliability Engineering and System Safety, Elsevier, vol. 189(C), pages 435-444.
    6. Chun, Hyonho & Lee, Myung Hee & Fleet, James C. & Oh, Ji Hwan, 2016. "Graphical models via joint quantile regression with component selection," Journal of Multivariate Analysis, Elsevier, vol. 152(C), pages 162-171.
    7. Patton, Andrew J., 2012. "A review of copula models for economic time series," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 4-18.
    8. Quessy, Jean-François & Bahraoui, Tarik, 2014. "Weak convergence of empirical and bootstrapped C-power processes and application to copula goodness-of-fit," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 16-36.
    9. Yandan Yang & Hon Keung Tony Ng & Narayanaswamy Balakrishnan, 2019. "Expectation–maximization algorithm for system-based lifetime data with unknown system structure," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(1), pages 69-98, March.
    10. Elena Di Bernardino & Didier Rullière, 2017. "A note on upper-patched generators for Archimedean copulas," Post-Print hal-01347869, HAL.
    11. Antonov I. N. & Knyazev A. G. & Lepekhin O. A., 2016. "Copula Models of the Joint Distribution of Exchange Rates," World of economics and management / Vestnik NSU. Series: Social and Economics Sciences, Socionet, vol. 16(4), pages 20-38.
    12. Di Bernardino Elena & Rullière Didier, 2013. "On certain transformations of Archimedean copulas: Application to the non-parametric estimation of their generators," Dependence Modeling, De Gruyter, vol. 1(2013), pages 1-36, October.
    13. Vadim Semenikhine & Edward Furman & Jianxi Su, 2018. "On a Multiplicative Multivariate Gamma Distribution with Applications in Insurance," Risks, MDPI, vol. 6(3), pages 1-20, August.
    14. Hofert, Marius, 2021. "Right-truncated Archimedean and related copulas," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 79-91.
    15. Elena Di Bernardino & Didier Rullière, 2016. "On tail dependence coefficients of transformed multivariate Archimedean copulas," Post-Print hal-00992707, HAL.
    16. Erhard Cramer & Jorge Navarro, 2015. "Progressive Type‐II censoring and coherent systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(6), pages 512-530, September.
    17. Ostap Okhrin & Anastasija Tetereva, 2017. "The Realized Hierarchical Archimedean Copula in Risk Modelling," Econometrics, MDPI, vol. 5(2), pages 1-31, June.
    18. Segers, Johan & Uyttendaele, Nathan, 2013. "Nonparametric estimation of the tree structure of a nested Archimedean copula," LIDAM Discussion Papers ISBA 2013009, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    19. M. Chahkandi & Jafar Ahmadi & S. Baratpour, 2014. "Non-parametric prediction intervals for the lifetime of coherent systems," Statistical Papers, Springer, vol. 55(4), pages 1019-1034, November.
    20. Bücher, Axel & Dette, Holger & Volgushev, Stanislav, 2012. "A test for Archimedeanity in bivariate copula models," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 121-132.

    More about this item

    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:wly:navres:v:59:y:2012:i:7:p:487-496. 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: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1520-6750 .

    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.