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.