Mean time to failure (MTTF) function plays an important role in connection with age replacement policy. In this paper, a goodness of fit test is proposed for MTTF function utilizing a weighted integral as a measure of deviation. The test statistic is shown to be asymptotically normal and the consistency of the test is also established. The proposed test is compared with some parametric tests of exponentiality in the sense of Pitman Asymptotic Relative Efficiency (PARE). The performance of the test is assessed by means of a simulation study. Finally, the test is applied to a real-life data set for illustrative purposes and the results are shown to be in accordance with those obtained by applying the one-sample Kolmogorov-Smirnov test.

平均无故障时间 (MTTF) 函数在与年龄替换政策相关的方面起着重要作用。在本文中，提出了使用加权积分作为偏差度量的 MTTF 函数的拟合优度测试。检验统计量显示为渐近正态，并且还建立了检验的一致性。将提议的检验与 Pitman 渐近相对效率 (PARE) 意义上的一些指数参数检验进行比较。测试的性能通过模拟研究进行评估。最后，出于说明目的，将测试应用于现实数据集，结果显示与通过应用单样本 Kolmogorov-Smirnov 测试获得的结果一致。