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Estimation of Stress-Strength Reliability for Multicomponent System with Rayleigh Data

Author

Listed:
  • Liang Wang

    (School of Mathematics, Yunnan Normal University, Kunming 650500, China
    These authors contributed equally to this work.)

  • Huizhong Lin

    (School of Mathematics, Yunnan Normal University, Kunming 650500, China
    These authors contributed equally to this work.)

  • Kambiz Ahmadi

    (Department of Computer Science, Faculty of Mathematical Sciences, Shahrekord University, Shahrekord 115, Iran
    These authors contributed equally to this work.)

  • Yuhlong Lio

    (Department of Mathematical Sciences, University of South Dakota, Vermillion, SD 57069, USA
    These authors contributed equally to this work.)

Abstract

Inference is investigated for a multicomponent stress-strength reliability (MSR) under Type-II censoring when the latent failure times follow two-parameter Rayleigh distribution. With a context that the lifetimes of the strength and stress variables have common location parameters, maximum likelihood estimator of MSR along with the existence and uniqueness is established. The associated approximate confidence interval is provided via the asymptotic distribution theory and delta method. Meanwhile, alternative generalized pivotal quantities-based point and confidence interval estimators are also constructed for MSR. More generally, when the lifetimes of strength and stress variables follow Rayleigh distributions with unequal location parameters, likelihood and generalized pivotal-based estimators are provided for MSR as well. In addition, to compare the equivalence of different strength and stress parameters, a likelihood ratio test is provided. Finally, simulation studies and a real data example are presented for illustration.

Suggested Citation

  • Liang Wang & Huizhong Lin & Kambiz Ahmadi & Yuhlong Lio, 2021. "Estimation of Stress-Strength Reliability for Multicomponent System with Rayleigh Data," Energies, MDPI, vol. 14(23), pages 1-23, November.
    • Handle: RePEc:gam:jeners:v:14:y:2021:i:23:p:7917-:d:687796
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    References listed on IDEAS

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    1. Fatih Kızılaslan, 2018. "Classical and Bayesian estimation of reliability in a multicomponent stress–strength model based on a general class of inverse exponentiated distributions," Statistical Papers, Springer, vol. 59(3), pages 1161-1192, September.
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    3. Fatih Kızılaslan & Mustafa Nadar, 2018. "Estimation of reliability in a multicomponent stress–strength model based on a bivariate Kumaraswamy distribution," Statistical Papers, Springer, vol. 59(1), pages 307-340, March.
    4. 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.
    5. Tanmay Kayal & Yogesh Mani Tripathi & Sanku Dey & Shuo-Jye Wu, 2020. "On estimating the reliability in a multicomponent stress-strength model based on Chen distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(10), pages 2429-2447, May.
    6. G. Srinivasa Rao & Muhammad Aslam & Debasis Kundu, 2015. "Burr-XII Distribution Parametric Estimation and Estimation of Reliability of Multicomponent Stress-Strength," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(23), pages 4953-4961, December.
    7. Nahed A. Mokhlis & Emad J. Ibrahim & Dina M. Gharieb, 2017. "Stress−strength reliability with general form distributions," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(3), pages 1230-1246, February.
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    Cited by:

    1. Yuhlong Lio & Tzong-Ru Tsai & Liang Wang & Ignacio Pascual Cecilio Tejada, 2022. "Inferences of the Multicomponent Stress–Strength Reliability for Burr XII Distributions," Mathematics, MDPI, vol. 10(14), pages 1-28, July.

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