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Reliability Assessment of Heavily Censored Data Based on E-Bayesian Estimation

Author

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  • Tianyu Liu

    (College of Systems Engineering, National University of Defense Technology, Changsha 410073, China)

  • Lulu Zhang

    (College of Systems Engineering, National University of Defense Technology, Changsha 410073, China)

  • Guang Jin

    (College of Systems Engineering, National University of Defense Technology, Changsha 410073, China)

  • Zhengqiang Pan

    (College of Systems Engineering, National University of Defense Technology, Changsha 410073, China)

Abstract

The classic E-Bayesian estimation methods can only derive point estimation of the reliability parameters. In this paper, an improved E-Bayesian estimation method is proposed to evaluate product reliability under heavily censored data, which can achieve both point and confidence interval estimation for the reliability parameters. Firstly, by analyzing the concavity & convexity and function characteristics of the Weibull distribution, the value of product failure probability is limited to a certain range. Secondly, an improved weighted least squares method is utilized to construct the confidence interval estimation model of reliability parameters. Simulation results show that the proposed approach can significantly improve the calculation speed and estimation accuracy with just very few robustness reductions. Finally, a real-world case study of the sun gear transmission mechanism is used to validate the effectiveness of the presented method.

Suggested Citation

  • Tianyu Liu & Lulu Zhang & Guang Jin & Zhengqiang Pan, 2022. "Reliability Assessment of Heavily Censored Data Based on E-Bayesian Estimation," Mathematics, MDPI, vol. 10(22), pages 1-14, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:22:p:4216-:d:969924
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    References listed on IDEAS

    as
    1. F. Yousefzadeh, 2017. "E-Bayesian and hierarchical Bayesian estimations for the system reliability parameter based on asymmetric loss function," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(1), pages 1-8, January.
    2. Ping Jiang & Yunyan Xing & Xiang Jia & Bo Guo, 2015. "Weibull Failure Probability Estimation Based on Zero-Failure Data," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-8, May.
    3. Joarder, Avijit & Krishna, Hare & Kundu, Debasis, 2011. "Inferences on Weibull parameters with conventional type-I censoring," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 1-11, January.
    4. Liesa Denecke & Christine Müller, 2014. "New robust tests for the parameters of the Weibull distribution for complete and censored data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(5), pages 585-607, July.
    5. Zhang, L.F. & Xie, M. & Tang, L.C., 2007. "A study of two estimation approaches for parameters of Weibull distribution based on WPP," Reliability Engineering and System Safety, Elsevier, vol. 92(3), pages 360-368.
    6. Tan, Zhibin, 2009. "A new approach to MLE of Weibull distribution with interval data," Reliability Engineering and System Safety, Elsevier, vol. 94(2), pages 394-403.
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    Cited by:

    1. Yongjun Chen & Xiaojian Li & Jin Wang & Mei Liu & Chaoxun Cai & Yuefeng Shi, 2023. "Research on the Application of Fuzzy Bayesian Network in Risk Assessment of Catenary Construction," Mathematics, MDPI, vol. 11(7), pages 1-19, April.

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