In this paper, we study a replacement model under which replacements take place not at fixed time but at random time T or upon failure. We study the properties of mean time to failure of the proposed model. Life times of two replacement models with different random replacement times have been compared using few stochastic orderings. A non-parametric test based on U-Statistics has been proposed for testing constancy of mean time to failure against NBUE alternative. The finite sample performance of the proposed test is evaluated through Monte Carlo simulation study. Finally, the proposed test procedure is illustrated using lifetime data of air conditioning equipment.

在本文中，我们研究了一种替换模型，在该模型下，替换不是在固定时间而是在随机时间T或失败时发生。我们研究了所提出模型的平均故障时间的特性。使用少量随机排序比较了具有不同随机替换时间的两种替换模型的寿命。已经提出了一种基于 U-Statistics 的非参数测试，用于测试针对 NBUE 替代方案的平均故障时间的恒定性。通过蒙特卡罗模拟研究评估了所提出的测试的有限样本性能。最后，使用空调设备的寿命数据说明了建议的测试程序。