For the purpose of improving the statistical efficiency of estimators in life-testing experiments, generalized Type-I hybrid censoring has lately been implemented by guaranteeing that experiments only terminate after a certain number of failures appear. With the wide applications of bathtub-shaped distribution in engineering areas and the recently introduced generalized Type-I hybrid censoring scheme, considering that there is no work coalescing this certain type of censoring model with a bathtub-shaped distribution, we consider the parameter inference under generalized Type-I hybrid censoring. First, estimations of the unknown scale parameter and the reliability function are obtained under the Bayesian method based on LINEX and squared error loss functions with a conjugate gamma prior. The comparison of estimations under the E-Bayesian method for different prior distributions and loss functions is analyzed. Additionally, Bayesian and E-Bayesian estimations with two unknown parameters are introduced. Furthermore, to verify the robustness of the estimations above, the Monte Carlo method is introduced for the simulation study. Finally, the application of the discussed inference in practice is illustrated by analyzing a real data set.

中文翻译：

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广义 I 型混合审查下浴缸形状分布的贝叶斯和 E-贝叶斯估计

为了提高寿命测试实验中估计器的统计效率，最近通过保证实验仅在出现一定数量的失败后才终止来实施广义 I 型混合删失。随着浴缸形分布在工程领域的广泛应用和最近引入的广义Type-I混合删失方案，考虑到没有工作将这种类型的删失模型与浴缸形分布合并，我们考虑下的参数推断广义 I 型混合审查。首先，基于LINEX和具有共轭伽玛先验的平方误差损失函数，在贝叶斯方法下获得未知尺度参数和可靠性函数的估计。分析了不同先验分布和损失函数在E-Bayesian方法下的估计比较。此外，还引入了具有两个未知参数的贝叶斯和 E-贝叶斯估计。此外，为了验证上述估计的稳健性，在模拟研究中引入了蒙特卡罗方法。最后，通过分析一个真实的数据集来说明所讨论的推理在实践中的应用。