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A random-effects Wiener degradation model based on accelerated failure time

机译：基于加速失效时间的随机效应维纳退化模型

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摘要

Due to the variability of raw materials and the fluctuation in the manufacturing process, degradation of products may exhibit unit-to-unit variability in a population. The heterogeneous degradation rates can be viewed as random effects, which are often modeled by a normal distribution. Despite of its mathematical convenience, the normal distribution has certain limitations in modeling the random effects. In this study, we propose a novel random-effects Wiener process model based on ideas from accelerated failure time principle. An inverse Gaussian (IG) distribution can be used to characterize the unit-specific heterogeneity in degradation paths, which overcomes the disadvantages of the traditional models and provides more flexibility in the degradation modeling using Wiener processes. Properties of the model are investigated, and statistical inference based on the maximum likelihood estimation and the EM algorithm is established. An extension of the model to the constant stress accelerated degradation test (ADT) is developed. The effectiveness and applicability of the proposed model are validated using a laser degradation dataset and an LED ADT dataset.
机译：由于原材料的可变性和制造过程中的波动，产品的降解可能会在人群中表现出单位间的可变性。异质降解速率可以看作是随机效应，通常通过正态分布来建模。尽管其数学上的便利性，但正态分布在对随机效应进行建模时具有一定的局限性。在这项研究中，我们根据加速失效时间原理提出了一种新颖的随机效应维纳过程模型。高斯逆（IG）分布可用于表征退化路径中特定于单元的异质性，这克服了传统模型的缺点，并在使用维纳过程的退化建模中提供了更大的灵活性。研究了模型的性质，建立了基于最大似然估计和EM算法的统计推断。将该模型扩展到恒应力加速退化测试（ADT）。使用激光降解数据集和LED ADT数据集验证了所提出模型的有效性和适用性。

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