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Inference for the Exponential Distribution under Generalized Progressively Hybrid Censored Data from Partially Accelerated Life Tests with a Time Transformation Function

Author

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  • Alaa H. Abdel-Hamid

    (Mathematics and Computer Science Department, Faculty of Science, Beni-Suef University, 62521 Beni-Suef, Egypt)

  • Atef F. Hashem

    (Mathematics and Computer Science Department, Faculty of Science, Beni-Suef University, 62521 Beni-Suef, Egypt
    ASRT, 101 Kasr Al-Aini ST, Academy of Scientific Research & Technology, 11516 Cairo, Egypt)

Abstract

In this article, the tampered failure rate model is used in partially accelerated life testing. A non-decreasing time function, often called a ‘ ‘ time transformation function", is proposed to tamper the failure rate under design conditions. Different types of the proposed function, which have sufficient conditions in order to be accelerating functions, are investigated. A baseline failure rate of the exponential distribution is considered. Some point estimation methods, as well as approximate confidence intervals, for the parameters involved are discussed based on generalized progressively hybrid censored data. The determination of the optimal stress change time is discussed under two different criteria of optimality. A real dataset is employed to explain the theoretical outcomes discussed in this article. Finally, a Monte Carlo simulation study is carried out to examine the performance of the estimation methods and the optimality criteria.

Suggested Citation

  • Alaa H. Abdel-Hamid & Atef F. Hashem, 2021. "Inference for the Exponential Distribution under Generalized Progressively Hybrid Censored Data from Partially Accelerated Life Tests with a Time Transformation Function," Mathematics, MDPI, vol. 9(13), pages 1-28, June.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:13:p:1510-:d:583897
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    References listed on IDEAS

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    1. Kundu, Debasis & Joarder, Avijit, 2006. "Analysis of Type-II progressively hybrid censored data," Computational Statistics & Data Analysis, Elsevier, vol. 50(10), pages 2509-2528, June.
    2. Abdel-Hamid, Alaa H. & AL-Hussaini, Essam K., 2009. "Estimation in step-stress accelerated life tests for the exponentiated exponential distribution with type-I censoring," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1328-1338, February.
    3. Arnab Koley & Debasis Kundu, 2017. "On generalized progressive hybrid censoring in presence of competing risks," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(4), pages 401-426, May.
    4. Essam AL-Hussaini & Alaa Abdel-Hamid & Atef Hashem, 2015. "One-sample Bayesian prediction intervals based on progressively type-II censored data from the half-logistic distribution under progressive stress model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(7), pages 771-783, October.
    5. Morris H. Degroot & Prem K. Goel, 1979. "Bayesian estimation and optimal designs in partially accelerated life testing," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 26(2), pages 223-235, June.
    6. Samanta, Debashis & Kundu, Debasis, 2018. "Order restricted inference of a multiple step-stress model," Computational Statistics & Data Analysis, Elsevier, vol. 117(C), pages 62-75.
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    Cited by:

    1. Atef F. Hashem & Salem A. Alyami & Alaa H. Abdel-Hamid, 2022. "Inference for a Progressive-Stress Model Based on Ordered Ranked Set Sampling under Type-II Censoring," Mathematics, MDPI, vol. 10(15), pages 1-23, August.

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