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Inference and Optimal Design on Partially Accelerated Life Tests for the Power Half-Logistic Distribution Under Adaptive Type II Progressive Censoring

Author

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  • Hanan Haj Ahmad

    (Department of Basic Science, The General Administration of Preparatory Year, King Faisal University, Hofuf 31982, Al-Ahsa, Saudi Arabia
    Department of Mathematics and Statistics, College of Science, King Faisal University, Hofuf 31982, Al-Ahsa, Saudi Arabia)

  • Mahmoud M. El-Awady

    (Basic Sciences Department, Misr Higher Institute for Commerce and Computers, Mansoura 35511, Egypt)

Abstract

This study explores accelerated life tests to examine the durability of highly reliable products. These tests involve applying higher stress levels, such as increased temperature, voltage, or pressure, that cause early failures. The power half-logistic (PHL) distribution is utilized due to its flexibility in modeling the probability density and hazard rate functions, effectively representing various data patterns commonly encountered in practical applications. The step stress partially accelerated life testing model is analyzed under an adaptive type II progressive censoring scheme, with samples drawn from the PHL distribution. The maximum likelihood method estimates model parameters and calculates asymptotic confidence intervals. Bayesian estimates are also obtained using Lindley’s approximation and the Markov Chain Monte Carlo (MCMC) method under different loss functions. Additionally, D- and A-optimality criteria are applied to determine the optimal stress-changing time. Simulation studies are conducted to evaluate the performance of the estimation methods and the optimality criteria. Finally, real-world datasets are analyzed to demonstrate the practical usefulness of the proposed model.

Suggested Citation

  • Hanan Haj Ahmad & Mahmoud M. El-Awady, 2025. "Inference and Optimal Design on Partially Accelerated Life Tests for the Power Half-Logistic Distribution Under Adaptive Type II Progressive Censoring," Mathematics, MDPI, vol. 13(3), pages 1-30, January.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:3:p:394-:d:1576786
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    References listed on IDEAS

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    2. Hon Keung Tony Ng & Debasis Kundu & Ping Shing Chan, 2009. "Statistical analysis of exponential lifetimes under an adaptive Type‐II progressive censoring scheme," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(8), pages 687-698, December.
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    6. 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.
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