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A new class of Wiener process models for degradation analysis

机译：用于降解分析的新型维纳过程模型

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For many products, it is not uncommon to see that a unit with a higher degradation rate has a more volatile degradation path. Motivated by this observation, we propose a new class of random effects model for the Wiener process model. We express the Wiener process in a special form and allow one of the parameters to be random across the product population so that a unit with a high degradation rate would also possess high volatility. Statistical inference of the model is discussed. By the same token, we introduce a stress-acceleration relation for the Wiener process so that both the degradation rate and the volatility of the product are increasing in the stress level. The proposed models are demonstrated by analyzing a dataset of fatigue crack growth and a dataset of head wears of hard disk drives. The applications suggest that our models perform better than existing models that ignore the positive correlation between the drift rate and the volatility. (C) 2015 Elsevier Ltd. All rights reserved.
机译：对于许多产品而言，看到具有较高降解率的设备具有更易挥发的降解路径的情况并不少见。基于这种观察，我们为维纳过程模型提出了一类新的随机效应模型。我们以一种特殊的形式表示维纳过程，并允许其中一个参数在整个产品群体中是随机的，因此具有较高降解率的装置也将具有较高的挥发性。讨论了模型的统计推断。同样，我们为维纳过程引入了应力-加速关系，以使产品的降解率和挥发性都在应力水平上增加。通过分析疲劳裂纹扩展数据集和硬盘驱动器磁头磨损数据集，证明了所提出的模型。这些应用表明，与忽略漂移率和波动率之间的正相关性的现有模型相比，我们的模型表现更好。 （C）2015 Elsevier Ltd.保留所有权利。

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