A doubly type-II censored scheme is an important sampling scheme in the life testing experiment and reliability engineering. In the present commutation, we have considered estimating ordered scale parameters of two exponential distributions based on doubly type-II censored samples with respect to a general scale invariant loss function. We have obtained several estimators that improve upon the BAEE. We also propose a class of improved estimators. It is shown that the boundary estimator of this class is generalized Bayes. As an application, we have derived improved estimators with respect to three special loss functions, namely quadratic loss, entropy loss, and symmetric loss function. We have applied these results to special life-testing sampling schemes. Finally, we conducted a simulation study to compare the performance of the improved estimators. A real-life data analysis has been considered for implementation purposes.

翻译：双II型截尾方案是寿命试验与可靠性工程中的重要抽样方案。本文基于双II型截尾样本，针对一般尺度不变损失函数，研究两个指数分布有序尺度参数的估计问题。我们获得了若干优于BAEE的估计量，并提出一类改进估计量。研究表明该类估计量的边界估计量具有广义贝叶斯性质。作为应用，我们针对三种特殊损失函数（二次损失、熵损失及对称损失函数）推导了改进估计量，并将这些结果应用于特殊寿命试验抽样方案。最后通过模拟研究比较了改进估计量的性能，并基于实际数据进行了应用分析。