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Reliability Estimation in a Multicomponent Stress-Strength Model Based on Inverse Weibull Distribution

Author

Listed:
  • Raj Kamal Maurya

    (Sardar Vallabhbhai National Institute of Technology)

  • Yogesh Mani Tripathi

    (Indian Institute of Technology Patna)

  • Tanmay Kayal

    (neurIOT Technologies LLP)

Abstract

Reliability inference in a multicomponent stress-strength (MSS) model is studied when components are exposed to a specific random stress. Stress and strength variables are assumed to follow inverse Weibull distributions with different scale and same shape parameter. A s-out-of-k:G system fails if s or more components simultaneously become inoperative. Different estimates of MSS reliability are obtained from frequentist and Bayesian viewpoint. In particular Bayes estimates are evaluated from Lindley method and Metropolis-Hastings algorithm. Unbiased estimation is also considered when shape parameter is known. We construct asymptotic intervals and obtain corresponding coverage probabilities using observed information matrix. In sequel credible intervals are also obtained. A simulation study is performed to examine the estimated risks of proposed estimation methods and analyze two numerical examples from application viewpoint. Finally, optimal plans are discussed for the multicomponent system.

Suggested Citation

  • Raj Kamal Maurya & Yogesh Mani Tripathi & Tanmay Kayal, 2022. "Reliability Estimation in a Multicomponent Stress-Strength Model Based on Inverse Weibull Distribution," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(1), pages 364-401, May.
    • Handle: RePEc:spr:sankhb:v:84:y:2022:i:1:d:10.1007_s13571-021-00263-0
    DOI: 10.1007/s13571-021-00263-0
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    References listed on IDEAS

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    1. Kundu, Debasis & Howlader, Hatem, 2010. "Bayesian inference and prediction of the inverse Weibull distribution for Type-II censored data," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1547-1558, June.
    2. 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.
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    Cited by:

    1. Neama Salah Youssef Temraz, 2023. "Inference on the stress strength reliability with exponentiated generalized Marshall Olkin-G distribution," PLOS ONE, Public Library of Science, vol. 18(8), pages 1-26, August.
    2. Amal S. Hassan & E. A. Elsherpieny & Rokaya E. Mohamed, 2025. "Bayesian Estimation of Stress Strength Modeling Using MCMC Method Based on Outliers," Annals of Data Science, Springer, vol. 12(1), pages 23-62, February.

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