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Reliability Estimation in Stress Strength for Generalized Rayleigh Distribution Using a Lower Record Ranked Set Sampling Scheme

Author

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  • Yinuo Dong

    (School of Mathematics and Statistics, Beijing Jiaotong University, Beijing 100044, China
    These authors contributed equally to this work.)

  • Wenhao Gui

    (School of Mathematics and Statistics, Beijing Jiaotong University, Beijing 100044, China
    These authors contributed equally to this work.)

Abstract

This paper explores the likelihood and Bayesian estimation of the stress–strength reliability parameter ( R ) based on a lower record ranked set sampling scheme from the generalized Rayleigh distribution. Maximum likelihood and Bayesian estimators as well as confidence intervals of R are derived and their properties are studied. Furthermore, two parametric bootstrap confidence intervals are introduced in the paper. A comparative simulation study is conducted to assess the effectiveness of these four confidence interval methodologies in estimating R . The application of the methods is demonstrated using real data on fiber strength to showcase their practicability and relevance in the industry.

Suggested Citation

  • Yinuo Dong & Wenhao Gui, 2024. "Reliability Estimation in Stress Strength for Generalized Rayleigh Distribution Using a Lower Record Ranked Set Sampling Scheme," Mathematics, MDPI, vol. 12(11), pages 1-15, May.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:11:p:1650-:d:1401085
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    References listed on IDEAS

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    1. Mahdi Rasekhi & Mohammad Mehdi Saber & Haitham M. Yousof, 2020. "Bayesian and classical inference of reliability in multicomponent stress-strength under the generalized logistic model," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 50(21), pages 5114-5125, September.
    2. McIntyre, G.A., 2005. "A Method for Unbiased Selective Sampling, Using Ranked Sets," The American Statistician, American Statistical Association, vol. 59, pages 230-232, August.
    3. Mahdi Salehi & Jafar Ahmadi, 2014. "Record ranked set sampling scheme," METRON, Springer;Sapienza Università di Roma, vol. 72(3), pages 351-365, October.
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