The performance and effectiveness of an age replacement policy can be assessed by its mean time to failure (MTTF) function. In this paper we propose a class of tests to detect trend change in MTTF function. We develop test statistics utilising a measure of deviation based on a weighted integral approach. We derive the exact and asymptotic distributions of our test statistics exploiting L-statistic theory and also establish the consistency of the test as a consequence of our results. A Monte Carlo study is conducted to evaluate the performance of the proposed test. Finally, we apply our test to some real life data sets for illustrative purposes.

中文翻译：

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针对非单调平均故障时间类型替代方案的指数精确和渐近检验

可以通过其平均失效时间（MTTF）功能来评估年龄替换策略的性能和有效性。在本文中，我们提出了一类测试来检测MTTF函数的趋势变化。我们基于加权积分方法利用偏差的度量来开发测试统计数据。我们利用L统计理论推导检验统计量的精确和渐近分布，并根据结果建立检验的一致性。进行了蒙特卡洛研究，以评估所提议测试的性能。最后，出于说明目的，我们将测试应用于一些现实生活中的数据集。