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Classical and Bayesian estimation of reliability in a multicomponent stress–strength model based on a general class of inverse exponentiated distributions

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  • Fatih Kızılaslan

    (Marmara University)

Abstract

A s-out-of-k : G system consists of k components functions if and only if at least s components functions. In this paper, we consider the s-out-of-k : G system when this system is exposed a common random stress and the underlying distributions belong to the family of inverse exponentiated distributions. The estimates of this sytem reliability are investigated by using classical and Bayesian approaches. The uniformly minimum variance unbiased and exact Bayes estimates of the reliability of system are obtained analytically when the common second parameter is known. The Bayes estimates for the reliability of system have been developed by using Lindley’s approximation and the Markov Chain Monte Carlo method due to the lack of explicit forms when the all parameters are unknown. The asymptotic confidence interval and coverage probabilities are derived based on the Fisher’s information matrix. The highest probability density credible interval is constructed by using the Markov Chain Monte Carlo method. The comparison of the derived estimates are carried out by using Monte Carlo simulations. Real data set is also analysed for an illustration of the findings.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stpapr:v:59:y:2018:i:3:d:10.1007_s00362-016-0810-7
    DOI: 10.1007/s00362-016-0810-7
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    References listed on IDEAS

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    1. Sanku Dey & Tanujit Dey, 2014. "On progressively censored generalized inverted exponential distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(12), pages 2557-2576, December.
    2. EryIlmaz, Serkan, 2010. "On system reliability in stress-strength setup," Statistics & Probability Letters, Elsevier, vol. 80(9-10), pages 834-839, May.
    3. 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.
    4. 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.
    5. Eryilmaz, Serkan, 2008. "Multivariate stress-strength reliability model and its evaluation for coherent structures," Journal of Multivariate Analysis, Elsevier, vol. 99(9), pages 1878-1887, October.
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    Cited by:

    1. Amulya Kumar Mahto & Yogesh Mani Tripathi, 2020. "Estimation of reliability in a multicomponent stress-strength model for inverted exponentiated Rayleigh distribution under progressive censoring," OPSEARCH, Springer;Operational Research Society of India, vol. 57(4), pages 1043-1069, December.
    2. 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.
    3. 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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