Yousef Manal M, Hassan Amal S, Almetwally Ehab M, Nagy M, Mansi A H
Department of Mathematics, Faculty of Science, New Valley University, El-Khargah, 72511, Egypt.
Faculty of Graduate Studies for Statistical Research, Cairo University, 12613, Giza, Egypt.
Sci Rep. 2025 Sep 17;15(1):32567. doi: 10.1038/s41598-025-06927-5.
Progressive-stress accelerated life testing (PSALT) is a specialized experimental method that evaluates the longevity of a product under continuously fluctuating stress levels. Due to the constraints of testing equipment and expenses, the lifetime data collected by PSALT are typically censored. This paper introduces the PSALT model that utilizes Type-II unified progressive hybrid censoring to address this data characteristic, specifically when the lifespan of test units follows a truncated Cauchy power exponential (TCPE) distribution. The distribution's scale parameter follows the inverse power law, and the cumulative exposure model is relevant for the effects of differing stress levels. The estimation methods for the TCPE parameters and the acceleration factor are examined, including maximum likelihood and Bayesian estimation techniques. Bayesian estimates are generated using the Markov chain Monte Carlo technique based on symmetric and asymmetric loss functions. The highest posterior density intervals are assessed, as well as asymptotic confidence intervals. A simulation study is conducted to evaluate the efficacy of the proposed point and interval estimators. Ultimately, a real data set is applied to the TCPE distribution, and the proposed estimators are assessed.
递进应力加速寿命试验（PSALT）是一种专门的实验方法，用于评估产品在不断波动的应力水平下的寿命。由于测试设备和费用的限制，PSALT收集的寿命数据通常是删失的。本文介绍了利用II型统一递进混合删失的PSALT模型来处理这种数据特征，特别是当测试单元的寿命服从截断柯西幂指数（TCPE）分布时。该分布的尺度参数遵循逆幂律，并且累积暴露模型与不同应力水平的影响相关。研究了TCPE参数和加速因子的估计方法，包括最大似然估计和贝叶斯估计技术。基于对称和非对称损失函数，使用马尔可夫链蒙特卡罗技术生成贝叶斯估计。评估了最高后验密度区间以及渐近置信区间。进行了模拟研究以评估所提出的点估计和区间估计的有效性。最终，将一个实际数据集应用于TCPE分布，并对所提出的估计器进行评估。
