IDEAS home Printed from https://ideas.repec.org/a/spr/testjl/v27y2018i3d10.1007_s11749-017-0564-0.html
   My bibliography  Save this article

Sharp inequalities for quantiles of system lifetime distributions from failure-dependent proportional hazard model

Author

Listed:
  • Marco Burkschat

    (RWTH Aachen University)

  • Tomasz Rychlik

    (Polish Academy of Sciences)

Abstract

We consider coherent systems with components whose exchangeable lifetime distributions come from the failure-dependent proportional hazard model, i.e., the consecutive failures satisfy the assumptions of the generalized order statistics model. For a fixed system and given failure rate proportion jumps, we provide sharp bounds on the deviations of system lifetime distribution quantiles from the respective quantiles of single component nominal and actual lifetime distributions. The bounds are expressed in the scale units generated by the absolute moments of various orders of the component lifetime centered about the median of its distribution.

Suggested Citation

  • Marco Burkschat & Tomasz Rychlik, 2018. "Sharp inequalities for quantiles of system lifetime distributions from failure-dependent proportional hazard model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(3), pages 618-638, September.
  • Handle: RePEc:spr:testjl:v:27:y:2018:i:3:d:10.1007_s11749-017-0564-0
    DOI: 10.1007/s11749-017-0564-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11749-017-0564-0
    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/s11749-017-0564-0?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. Marichal, Jean-Luc & Mathonet, Pierre & Waldhauser, Tamás, 2011. "On signature-based expressions of system reliability," Journal of Multivariate Analysis, Elsevier, vol. 102(10), pages 1410-1416, November.
    2. Erhard Cramer & Udo Kamps, 2003. "Marginal distributions of sequential and generalized order statistics," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 58(3), pages 293-310, December.
    3. Xue, Jing-Hao & Titterington, D. Michael, 2011. "The p-folded cumulative distribution function and the mean absolute deviation from the p-quantile," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1179-1182, August.
    4. Jorge Navarro, 2016. "Stochastic comparisons of generalized mixtures and coherent systems," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 150-169, March.
    5. Mariusz Bieniek, 2007. "Variation diminishing property of densities of uniform generalized order statistics," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 65(3), pages 297-309, May.
    6. Shaked, Moshe & Suarez-Llorens, Alfonso, 2003. "On the Comparison of Reliability Experiments Based on the Convolution Order," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 693-702, January.
    7. Jorge Navarro & Marco Burkschat, 2011. "Coherent systems based on sequential order statistics," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(2), pages 123-135, March.
    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. Mariusz Bieniek & Marco Burkschat & Tomasz Rychlik, 2020. "Comparisons of the Expectations of System and Component Lifetimes in the Failure Dependent Proportional Hazard Model," Methodology and Computing in Applied Probability, Springer, vol. 22(1), pages 173-189, March.
    2. Foschi Rachele & Nappo Giovanna & Spizzichino Fabio L., 2021. "Diagonal sections of copulas, multivariate conditional hazard rates and distributions of order statistics for minimally stable lifetimes," Dependence Modeling, De Gruyter, vol. 9(1), pages 394-423, January.
    3. Jorge Navarro & Rafael Rubio, 2011. "A note on necessary and sufficient conditions for ordering properties of coherent systems with exchangeable components," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(5), pages 478-489, August.
    4. Maryam Esna-Ashari & Narayanaswamy Balakrishnan & Mahdi Alimohammadi, 2023. "HR and RHR orderings of generalized order statistics," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(1), pages 131-148, January.
    5. Tzong-Ru Tsai & Hua Xin & Chiun-How Kao, 2021. "Bayesian Estimation Based on Sequential Order Statistics for Heterogeneous Baseline Gompertz Distributions," Mathematics, MDPI, vol. 9(2), pages 1-21, January.
    6. Tzong-Ru Tsai & Yuhlong Lio & Hua Xin & Hoang Pham, 2021. "Parameter Estimation for Composite Dynamical Systems Based on Sequential Order Statistics from Burr Type XII Mixture Distribution," Mathematics, MDPI, vol. 9(8), pages 1-17, April.
    7. Jorge Navarro, 2018. "Stochastic comparisons of coherent systems," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(4), pages 465-482, May.
    8. 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.
    9. Gaofeng Da & Lvyu Xia & Taizhong Hu, 2014. "On Computing Signatures of k-out-of-n Systems Consisting of Modules," Methodology and Computing in Applied Probability, Springer, vol. 16(1), pages 223-233, March.
    10. Zarezadeh, S. & Mohammadi, L. & Balakrishnan, N., 2018. "On the joint signature of several coherent systems with some shared components," European Journal of Operational Research, Elsevier, vol. 264(3), pages 1092-1100.
    11. Krzysztof Jasiński, 2021. "The number of failed components in a coherent working system when the lifetimes are discretely distributed," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(7), pages 1081-1094, October.
    12. van Bentum, Thomas & Cramer, Erhard, 2019. "Stochastic monotonicity of MLEs of the mean for exponentially distributed lifetimes under hybrid censoring," Statistics & Probability Letters, Elsevier, vol. 148(C), pages 1-8.
    13. Zhengcheng Zhang & N. Balakrishnan, 2016. "Representations of the inactivity time for coherent systems with heterogeneous components and some ordered properties," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(1), pages 113-126, January.
    14. Omid Shojaee & Majid Asadi & Maxim Finkelstein, 2021. "On Some Properties of $$\alpha $$ α -Mixtures," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(8), pages 1213-1240, November.
    15. Tomasz J. Kozubowski & Krzysztof Podgórski, 2018. "Kumaraswamy Distribution and Random Extrema," The Open Statistics and Probability Journal, Bentham Open, vol. 9(1), pages 18-25, July.
    16. Marichal, Jean-Luc & Mathonet, Pierre & Spizzichino, Fabio, 2015. "On modular decompositions of system signatures," Journal of Multivariate Analysis, Elsevier, vol. 134(C), pages 19-32.
    17. Amini, Morteza & Balakrishnan, N., 2013. "Nonparametric meta-analysis of independent samples of records," Computational Statistics & Data Analysis, Elsevier, vol. 66(C), pages 70-81.
    18. Marichal, Jean-Luc & Mathonet, Pierre, 2013. "On the extensions of Barlow–Proschan importance index and system signature to dependent lifetimes," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 48-56.
    19. Bedbur, Stefan & Johnen, Marcus & Kamps, Udo, 2019. "Inference from multiple samples of Weibull sequential order statistics," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 381-399.
    20. M. Burkschat & J. Navarro, 2014. "Asymptotic behavior of the hazard rate in systems based on sequential order statistics," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(8), pages 965-994, November.

    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:testjl:v:27:y:2018:i:3:d:10.1007_s11749-017-0564-0. 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.