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Bayesian Estimation Using MCMC Method of System Reliability for Inverted Topp–Leone Distribution Based on Ranked Set Sampling

Author

Listed:
  • Manal M. Yousef

    (Department of Mathematics, Faculty of Science, New Valley University, EL-Khargah 72511, Egypt
    These authors contributed equally to this work.)

  • Amal S. Hassan

    (Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, Egypt
    These authors contributed equally to this work.)

  • Abdullah H. Al-Nefaie

    (Quantitative Methods Department, School of Business, King Faisal University, Al Ahsa 31982, Saudi Arabia
    These authors contributed equally to this work.)

  • Ehab M. Almetwally

    (Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, Egypt
    Faculty of Business Administration, Delta University of Science and Technology, Gamasa 11152, Egypt
    The Scientific Association for Studies and Applied Research, Al Manzalah 35646, Egypt
    These authors contributed equally to this work.)

  • Hisham M. Almongy

    (Department of Applied Statistics and Insurance, Faculty of Commerce, Mansoura University, Mansoura 35516, Egypt
    These authors contributed equally to this work.)

Abstract

The current work focuses on ranked set sampling and a simple random sample as sampling approaches for determining stress–strength reliability from the inverted Topp–Leone distribution. Asymptotic confidence intervals are established, along with a maximum likelihood estimator of the parameters and stress–strength reliability. The reliability of such a system is assessed using the Bayesian approach under symmetric and asymmetric loss functions. The highest posterior density credible interval is constructed successively. The results are extracted using Monte Carlo simulation to compare the proposed estimators performance with different sample sizes. Finally, by looking at waiting time data and failure times of insulating fluid, the usefulness of the suggested technique is demonstrated.

Suggested Citation

  • Manal M. Yousef & Amal S. Hassan & Abdullah H. Al-Nefaie & Ehab M. Almetwally & Hisham M. Almongy, 2022. "Bayesian Estimation Using MCMC Method of System Reliability for Inverted Topp–Leone Distribution Based on Ranked Set Sampling," Mathematics, MDPI, vol. 10(17), pages 1-26, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:17:p:3122-:d:902777
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    References listed on IDEAS

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    1. M. E. Ghitany & D. K. Al-Mutairi, 2008. "Size-biased Poisson-Lindley distribution and its application," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 299-311.
    2. Mohamed Aboraya & Haitham M. Yousof & G.G. Hamedani & Mohamed Ibrahim, 2020. "A New Family of Discrete Distributions with Mathematical Properties, Characterizations, Bayesian and Non-Bayesian Estimation Methods," Mathematics, MDPI, vol. 8(10), pages 1-25, September.
    3. Jessie Marie Byrnes & Yu-Jau Lin & Tzong-Ru Tsai & Yuhlong Lio, 2019. "Bayesian Inference of δ = P ( X < Y ) for Burr Type XII Distribution Based on Progressively First Failure-Censored Samples," Mathematics, MDPI, vol. 7(9), pages 1-24, September.
    4. Ehsan Zamanzade, 2019. "EDF-based tests of exponentiality in pair ranked set sampling," Statistical Papers, Springer, vol. 60(6), pages 2141-2159, December.
    5. Amal S. Hassan & Rasha S. Elshaarawy & Ronald Onyango & Heba F. Nagy & Nawab Hussain, 2022. "Estimating System Reliability Using Neoteric and Median RSS Data for Generalized Exponential Distribution," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2022, pages 1-17, March.
    6. Amer Ibrahim Al-Omari & Amal S. Hassan & Naif Alotaibi & Mansour Shrahili & Heba F. Nagy, 2021. "Reliability Estimation of Inverse Lomax Distribution Using Extreme Ranked Set Sampling," Advances in Mathematical Physics, Hindawi, vol. 2021, pages 1-12, December.
    7. 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.
    8. Liang Wang & Xuanjia Zuo & Yogesh Mani Tripathi & Junyuan Wang, 2020. "Reliability analysis for stress-strength model from a general family of truncated distributions under censored data," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(15), pages 3589-3608, August.
    9. Al-Saleh, M. Fraiwan & Al-Kadiri, M. Ali, 2000. "Double-ranked set sampling," Statistics & Probability Letters, Elsevier, vol. 48(2), pages 205-212, June.
    10. Cesar Augusto Taconeli & Wagner Hugo Bonat, 2020. "On the performance of estimation methods under ranked set sampling," Computational Statistics, Springer, vol. 35(4), pages 1805-1826, December.
    11. Ibrahim Elbatal & Naif Alotaibi & Salem A. Alyami & Mohammed Elgarhy & Ahmed R. El-Saeed, 2022. "Bayesian and Non-Bayesian Estimation of the Nadaraj ah–Haghighi Distribution: Using Progressive Type-1 Censoring Scheme," Mathematics, MDPI, vol. 10(5), pages 1-16, February.
    12. Ghitany, M.E. & Al-Mutairi, D.K. & Nadarajah, S., 2008. "Zero-truncated Poisson–Lindley distribution and its application," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(3), pages 279-287.
    13. Ghitany, M.E. & Atieh, B. & Nadarajah, S., 2008. "Lindley distribution and its application," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 78(4), pages 493-506.
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    Cited by:

    1. Amal S. Hassan & Ibrahim M. Almanjahie & Amer Ibrahim Al-Omari & Loai Alzoubi & Heba Fathy Nagy, 2023. "Stress–Strength Modeling Using Median-Ranked Set Sampling: Estimation, Simulation, and Application," Mathematics, MDPI, vol. 11(2), pages 1-19, January.
    2. Heba F. Nagy & Amer Ibrahim Al-Omari & Amal S. Hassan & Ghadah A. Alomani, 2022. "Improved Estimation of the Inverted Kumaraswamy Distribution Parameters Based on Ranked Set Sampling with an Application to Real Data," Mathematics, MDPI, vol. 10(21), pages 1-19, November.

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