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Reliability Inference for the Multicomponent System Based on Progressively Type II Censored Samples from Generalized Pareto Distributions

Author

Listed:
  • Lauren Sauer

    (Department of Mathematical Sciences, University of South Dakota, Vermillion, SD 57069, USA)

  • Yuhlong Lio

    (Department of Mathematical Sciences, University of South Dakota, Vermillion, SD 57069, USA)

  • Tzong-Ru Tsai

    (Department of Statistics, Tamkang University, Tamsui District, New Taipei City 251301, Taiwan)

Abstract

In this paper, the reliability of a k -component system, in which all components are subject to common stress, is considered. The multicomponent system will continue to survive if at least s out of k components’ strength exceed the common stress. The system reliability is investigated by utilizing the maximum likelihood estimator based on progressively type II censored samples from generalized Pareto distributions. The confidence interval of the system reliability can be obtained by using asymptotic normality with Fisher information matrix or bootstrap method approximation. An intensive simulation study is conducted to evaluate the performance of maximum likelihood estimators of the model parameters and system reliability for a variety of cases. For the confidence interval of the system reliability, simulation results indicate the bootstrap method approximation outperforms over the asymptotic normality approximation in terms of coverage probability.

Suggested Citation

  • Lauren Sauer & Yuhlong Lio & Tzong-Ru Tsai, 2020. "Reliability Inference for the Multicomponent System Based on Progressively Type II Censored Samples from Generalized Pareto Distributions," Mathematics, MDPI, vol. 8(7), pages 1-14, July.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:7:p:1176-:d:386042
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    References listed on IDEAS

    as
    1. Wu, Shuo-Jye & Kus, Coskun, 2009. "On estimation based on progressive first-failure-censored sampling," Computational Statistics & Data Analysis, Elsevier, vol. 53(10), pages 3659-3670, August.
    2. 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.
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    Cited by:

    1. Shubham Saini & Renu Garg, 2022. "Reliability inference for multicomponent stress–strength model from Kumaraswamy-G family of distributions based on progressively first failure censored samples," Computational Statistics, Springer, vol. 37(4), pages 1795-1837, September.

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