On the basis of the principle of degradation mechanism invariance, a Wiener degradation process with random drift parameter is used to model the data collected from the constant stress accelerated degradation test. Small‐sample statistical inference method for this model is proposed. On the basis of Fisher's method, a test statistic is proposed to test if there is unit‐to‐unit variability in the population. For reliability inference, the quantities of interest are the quantile function, the reliability function, and the mean time to failure at the designed stress level. Because it is challenging to obtain exact confidence intervals (CIs) for these quantities, a regression type of model is used to construct pivotal quantities, and we develop generalized confidence intervals (GCIs) procedure for those quantities of interest. Generalized prediction interval for future degradation value at designed stress level is also discussed. A Monte Carlo simulation study is used to demonstrate the benefits of our procedures. Through simulation comparison, it is found that the coverage proportions of the proposed GCIs are better than that of the Wald CIs and GCIs have good properties even when there are only a small number of test samples available. Finally, a real example is used to illustrate the developed procedures.

中文翻译：

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基于具有随机效应的维纳过程的加速降解数据的可靠性分析

根据退化机制不变性的原理，采用具有随机漂移参数的Wiener退化过程对从恒应力加速退化测试收集的数据进行建模。提出了该模型的小样本统计推断方法。在费舍尔方法的基础上，提出了检验统计量，以检验总体中是否存在单位间的变异性。对于可靠性推断，关注的数量是分位数函数，可靠性函数以及在设计应力水平下的平均失效时间。由于获取这些数量的确切置信区间（CI）具有挑战性，因此使用一种回归类型的模型来构造关键数量，并且我们针对这些感兴趣的数量开发广义置信区间（GCI）程序。还讨论了在设计应力水平下对未来退化值的广义预测间隔。蒙特卡洛模拟研究用于证明我们程序的好处。通过仿真比较发现，所提出的GCI的覆盖率要比Wald CI的好，并且即使只有少量的测试样品，GCI仍具有良好的性能。最后，使用一个真实的例子来说明开发的过程。可以发现，提出的GCI的覆盖率要比Wald CI的好，并且即使只有少量的测试样品，GCI也具有良好的性能。最后，使用一个真实的例子来说明开发的过程。可以发现，提出的GCI的覆盖率要比Wald CI的好，并且即使只有少量的测试样品，GCI也具有良好的性能。最后，使用一个真实的例子来说明开发的过程。