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Accelerated Life Tests under Pareto-IV Lifetime Distribution: Real Data Application and Simulation Study

Author

Listed:
  • A. M. Abd El-Raheem

    (Department of Mathematics, Faculty of Education, Ain Shams University, Cairo 11566, Egypt)

  • M. H. Abu-Moussa

    (Department of Mathematics, Faculty of Science, Cairo University, Giza 12511, Egypt)

  • Marwa M. Mohie El-Din

    (Department of Mathematics, Faculty of Engineering, Egyptian Russian University, Cairo 11829, Egypt)

  • E. H. Hafez

    (Department of Mathematics, Faculty of Science, Helwan University, Cairo 11795, Egypt)

Abstract

In this article, a progressive-stress accelerated life test (ALT) that is based on progressive type-II censoring is studied. The cumulative exposure model is used when the lifetime of test units follows Pareto-IV distribution. Different estimates as the maximum likelihood estimates (MLEs) and Bayes estimates (BEs) for the model parameters are discussed. Bayesian estimates are derived while using the Tierney and Kadane (TK) approximation method and the importance sampling method. The asymptotic and bootstrap confidence intervals (CIs) of the parameters are constructed. A real data set is analyzed in order to clarify the methods proposed through this paper. Two types of the progressive-stress tests, the simple ramp-stress test and multiple ramp-stress test, are compared through the simulation study. Finally, some interesting conclusions are drawn.

Suggested Citation

  • A. M. Abd El-Raheem & M. H. Abu-Moussa & Marwa M. Mohie El-Din & E. H. Hafez, 2020. "Accelerated Life Tests under Pareto-IV Lifetime Distribution: Real Data Application and Simulation Study," Mathematics, MDPI, vol. 8(10), pages 1-19, October.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:10:p:1786-:d:428425
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    References listed on IDEAS

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    5. M. M. Mohie El-Din & S. E. Abu-Youssef & Nahed S. A. Ali & A. M. Abd El-Raheem, 2016. "Estimation in constant-stress accelerated life tests for extension of the exponential distribution under progressive censoring," METRON, Springer;Sapienza Università di Roma, vol. 74(2), pages 253-273, August.
    6. Alaa Abdel-Hamid & Essam AL-Hussaini, 2007. "Progressive stress accelerated life tests under finite mixture models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 66(2), pages 213-231, September.
    7. Z. F. Jaheen & H. M. Moustafa & G. H. Abd El-Monem, 2014. "Bayes Inference in Constant Partially Accelerated Life Tests for the Generalized Exponential Distribution with Progressive Censoring," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 43(14), pages 2973-2988, July.
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    Cited by:

    1. Sara O. Abd El-Azeem & Mahmoud H. Abu-Moussa & Moustafa M. Mohie El-Din & Lamiaa S. Diab, 2024. "On Step-Stress Partially Accelerated Life Testing with Competing Risks Under Progressive Type-II Censoring," Annals of Data Science, Springer, vol. 11(3), pages 909-930, June.
    2. Abdalla Abdel-Ghaly & Hanan Aly & Elham Abdel-Rahman, 2023. "Bayesian Inference Under Ramp Stress Accelerated Life Testing Using Stan," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 132-174, May.

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