Accelerated life testing is an efficient tool frequently adopted for obtaining failure time data of test units in a lesser time period as compared to normal use conditions. We assume that the lifetime data of a product at constant level of stress follows an exponentiated Poisson-exponential distribution and the shape parameter of the model has a log-linear relationship with the stress level. Model parameters, the reliability function (RF), and the mean time to failure (MTTF) function under use conditions are estimated based on eight frequentist methods of estimation, namely, method of maximum likelihood, method of least square and weighted least square, method of maximum product of spacing, method of minimum spacing absolute-log distance, method of Cramér-von-Mises, method of Anderson–Darling, and Right-tail Anderson–Darling. The performance of the different estimation methods is evaluated in terms of their mean relative estimate and mean squared error using small and large sample sizes through a Monte Carlo simulation study. Finally, two accelerated life test data sets are considered and bootstrap confidence intervals for the unknown parameters, predicted shape parameter, predicted RF, and the MTTF at different stress levels, are obtained.

中文翻译：

---

指数泊松-指数恒应力加速寿命试验模型的可靠性分析

加速寿命测试是一种经常采用的有效工具，用于在与正常使用条件相比更短的时间内获取测试单元的故障时间数据。我们假设产品在恒定应力水平下的寿命数据遵循指数泊松指数分布，并且模型的形状参数与应力水平具有对数线性关系。使用条件下的模型参数、可靠性函数（RF）和平均故障时间（MTTF）函数是基于八种频率估计方法进行估计的，即最大似然法、最小二乘法和加权最小二乘法、法最大间距乘积法、最小间距绝对对数距离法、Cramér-von-Mises 法、Anderson-Darling 法和 Right-tail Anderson-Darling 法。通过蒙特卡罗模拟研究，使用小样本和大样本，根据平均相对估计和均方误差评估不同估计方法的性能。最后，考虑了两个加速寿命测试数据集，并获得了未知参数、预测形状参数、预测 RF 和不同应力水平下的 MTTF 的自举置信区间。