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Stress–Strength Modeling Using Median-Ranked Set Sampling: Estimation, Simulation, and Application

Author

Listed:
  • Amal S. Hassan

    (Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, Egypt)

  • Ibrahim M. Almanjahie

    (Department of Mathematics, College of Science, King Khalid University, Abha 62529, Saudi Arabia)

  • Amer Ibrahim Al-Omari

    (Department of Mathematics, Faculty of Science, Al Albayt University, Mafraq 25113, Jordan)

  • Loai Alzoubi

    (Department of Mathematics, Faculty of Science, Al Albayt University, Mafraq 25113, Jordan)

  • Heba Fathy Nagy

    (Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, Egypt)

Abstract

In this study, we look at how to estimate stress–strength reliability models, R 1 = P ( Y < X ) and R 2 = P ( Y < X ), where the strength X and stress Y have the same distribution in the first model, R 1 , and strength X and stress Z have different distributions in the second model, R 2 . Based on the first model, the stress Y and strength X are assumed to have the Lomax distributions, whereas, in the second model, X and Z are assumed to have both the Lomax and inverse Lomax distributions, respectively. With the assumption that the variables in both models are independent, the median-ranked set sampling (MRSS) strategy is used to look at different possibilities. Using the maximum likelihood technique and an MRSS design, we derive the reliability estimators for both models when the strength and stress variables have a similar or dissimilar set size. The simulation study is used to verify the accuracy of various estimates. In most cases, the simulation results show that the reliability estimates for the second model are more efficient than those for the first model in the case of dissimilar set sizes. However, with identical set sizes, the reliability estimates for the first model are more efficient than the equivalent estimates for the second model. Medical data are used for further illustration, allowing the theoretical conclusions to be verified.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:2:p:318-:d:1028221
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    References listed on IDEAS

    as
    1. 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.
    2. Chahkandi, M. & Ganjali, M., 2009. "On some lifetime distributions with decreasing failure rate," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4433-4440, October.
    3. Ehsan Zamanzade, 2019. "EDF-based tests of exponentiality in pair ranked set sampling," Statistical Papers, Springer, vol. 60(6), pages 2141-2159, December.
    4. 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.
    5. Safar M. Alghamdi & Rashad A. R. Bantan & Amal S. Hassan & Heba F. Nagy & Ibrahim Elbatal & Mohammed Elgarhy, 2022. "Improved EDF-Based Tests for Weibull Distribution Using Ranked Set Sampling," Mathematics, MDPI, vol. 10(24), pages 1-24, December.
    6. 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.
    7. 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.
    8. Abhimanyu Singh Yadav & Sanjay Kumar Singh & Umesh Singh, 2016. "On Hybrid Censored Inverse Lomax Distribution: Application to the Survival Data," Statistica, Department of Statistics, University of Bologna, vol. 76(2), pages 185-203.
    9. M. Ahsanullah, 1991. "Record values of the Lomax distribution," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 45(1), pages 21-29, March.
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