IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v191y2022icp95-119.html
   My bibliography  Save this article

Interval estimation of multicomponent stress–strength reliability based on inverse Weibull distribution

Author

Listed:
  • Jana, Nabakumar
  • Bera, Samadrita

Abstract

This paper considers interval estimation of stress–strength reliability of k-out-of-n system when the stress and strength components follow inverse Weibull distributions. Besides the asymptotic and bootstrap confidence intervals, we derive HPD credible intervals when the shape parameter is known or unknown. We also propose the pivotal quantity and generalized confidence interval of reliability. We study the estimation of multicomponent stress–strength reliability using lower record values. Generalized, asymptotic, and bootstrap confidence intervals are derived using lower record values. We also derive confidence intervals of multicomponent stress–strength reliability assuming the shape parameters are different. We propose HPD credible intervals, generalized and bootstrap confidence intervals. Monte Carlo simulation is performed to compare the confidence intervals. Real data examples are presented to demonstrate the practicability of the confidence intervals.

Suggested Citation

  • Jana, Nabakumar & Bera, Samadrita, 2022. "Interval estimation of multicomponent stress–strength reliability based on inverse Weibull distribution," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 191(C), pages 95-119.
    • Handle: RePEc:eee:matcom:v:191:y:2022:i:c:p:95-119
    DOI: 10.1016/j.matcom.2021.07.026
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475421002767
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2021.07.026?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. Wang, Bing Xing & Yu, Keming & Coolen, Frank P.A., 2015. "Interval estimation for proportional reversed hazard family based on lower record values," Statistics & Probability Letters, Elsevier, vol. 98(C), pages 115-122.
    2. Wang, Bing Xing & Ye, Zhi-Sheng, 2015. "Inference on the Weibull distribution based on record values," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 26-36.
    3. Gupta, Ramesh C. & Ghitany, M.E. & Al-Mutairi, D.K., 2012. "Estimation of reliability in a parallel system with random sample size," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 83(C), pages 44-55.
    4. Baklizi, Ayman, 2008. "Likelihood and Bayesian estimation of using lower record values from the generalized exponential distribution," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3468-3473, March.
    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. Nabakumar Jana & Samadrita Bera, 2024. "Estimation of multicomponent system reliability for inverse Weibull distribution using survival signature," Statistical Papers, Springer, vol. 65(8), pages 5077-5108, October.

    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. Kızılaslan, Fatih, 2017. "Classical and Bayesian estimation of reliability in a multicomponent stress–strength model based on the proportional reversed hazard rate mode," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 136(C), pages 36-62.
    2. Khan, Ruhul Ali, 2023. "Two-sample nonparametric test for proportional reversed hazards," Computational Statistics & Data Analysis, Elsevier, vol. 182(C).
    3. Christina Empacher & Udo Kamps & Grigoriy Volovskiy, 2023. "Statistical Prediction of Future Sports Records Based on Record Values," Stats, MDPI, vol. 6(1), pages 1-17, January.
    4. Wang, Bing Xing & Ye, Zhi-Sheng, 2015. "Inference on the Weibull distribution based on record values," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 26-36.
    5. William Volterman & R. Arabi Belaghi & N. Balakrishnan, 2018. "Joint records from two exponential populations and associated inference," Computational Statistics, Springer, vol. 33(1), pages 549-562, March.
    6. Ayush Tripathi & Umesh Singh & Sanjay Kumar Singh, 2021. "Inferences for the DUS-Exponential Distribution Based on Upper Record Values," Annals of Data Science, Springer, vol. 8(2), pages 387-403, June.
    7. Wong, Augustine C.M. & Wu, Yan Yan, 2009. "A note on interval estimation of P(X," Computational Statistics & Data Analysis, Elsevier, vol. 53(10), pages 3650-3658, August.
    8. Liu, Yiming & Shi, Yimin & Bai, Xuchao & Zhan, Pei, 2018. "Reliability estimation of a N-M-cold-standby redundancy system in a multicomponent stress–strength model with generalized half-logistic distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 231-249.
    9. Liang Wang & Huizhong Lin & Yuhlong Lio & Yogesh Mani Tripathi, 2022. "Interval Estimation of Generalized Inverted Exponential Distribution under Records Data: A Comparison Perspective," Mathematics, MDPI, vol. 10(7), pages 1-20, March.
    10. Francesca Condino & Filippo Domma & Giovanni Latorre, 2018. "Likelihood and Bayesian estimation of $$P(Y{," Statistical Papers, Springer, vol. 59(2), pages 467-485, June.
    11. A. James & N. Chandra & Nicy Sebastian, 2023. "Stress-strength reliability estimation for bivariate copula function with rayleigh marginals," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 14(1), pages 196-215, March.
    12. A. Asgharzadeh & M. Kazemi & D. Kundu, 2017. "Estimation of $$P(X>Y)$$ P ( X > Y ) for Weibull distribution based on hybrid censored samples," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 8(1), pages 489-498, January.
    13. Wang, Bing Xing & Yu, Keming & Coolen, Frank P.A., 2015. "Interval estimation for proportional reversed hazard family based on lower record values," Statistics & Probability Letters, Elsevier, vol. 98(C), pages 115-122.
    14. Abhimanyu Singh Yadav & S. K. Singh & Umesh Singh, 2019. "Bayesian estimation of $$R=P[Y," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 10(5), pages 905-917, October.
    15. Saralees Nadarajah, 2011. "The exponentiated exponential distribution: a survey," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 95(3), pages 219-251, September.
    16. Mustafa Nadar & Fatih Kızılaslan, 2014. "Classical and Bayesian estimation of $$P(X>Y)$$ P ( X > Y ) using upper record values from Kumaraswamy’s distribution," Statistical Papers, Springer, vol. 55(3), pages 751-783, August.
    17. Jeongwook Lee & Joon Jin Song & Yongku Kim & Jung In Seo, 2020. "Estimation and Prediction of Record Values Using Pivotal Quantities and Copulas," Mathematics, MDPI, vol. 8(10), pages 1-16, October.
    18. EryIlmaz, Serkan, 2010. "On system reliability in stress-strength setup," Statistics & Probability Letters, Elsevier, vol. 80(9-10), pages 834-839, May.
    19. M. S. Kotb & M. Z. Raqab, 2021. "Estimation of reliability for multi-component stress–strength model based on modified Weibull distribution," Statistical Papers, Springer, vol. 62(6), pages 2763-2797, December.

    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:matcom:v:191:y:2022:i:c:p:95-119. 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.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.