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Inferences of the Multicomponent Stress–Strength Reliability for Burr XII Distributions

Author

Listed:
  • Yuhlong Lio

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

  • Tzong-Ru Tsai

    (Department of Statistics, Tamkang University, Tamsui District, New Taipei City 25137, Taiwan
    These authors contributed equally to this work.)

  • Liang Wang

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

  • Ignacio Pascual Cecilio Tejada

    (Department of Mathematics, Universidad de Almería, 04120 Almería, Spain
    These authors contributed equally to this work.)

Abstract

Multicomponent stress–strength reliability (MSR) is explored for the system with Burr XII distributed components under Type-II censoring. When the distributions of strength and stress variables have Burr XII distributions with common or unequal inner shape parameters, the existence and uniqueness of the maximum likelihood estimators are investigated and established. The associated approximate confidence intervals are obtained by using the asymptotic normal distribution theory along with the delta method and parametric bootstrap procedure, respectively. Moreover, alternative generalized pivotal quantities-based point and confidence interval estimators are developed. Additionally, a likelihood ratio test is presented to diagnose the equivalence of both inner shape parameters or not. Conclusively, Monte Carlo simulations and real data analysis are conducted for illustration.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:14:p:2478-:d:864202
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    References listed on IDEAS

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    1. 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.
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    10. Y. L. Lio & Tzong-Ru Tsai, 2012. "Estimation of δ= P ( X > Y ) for Burr XII distribution based on the progressively first failure-censored samples," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(2), pages 309-322, April.
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    Cited by:

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