Accelerated degradation testing (ADT) is an effective way to evaluate the reliability and lifetime of highly reliable products. Existing studies have shown that the degradation processes of some products are non-Markovian with long-range dependence due to the interaction with environments. Besides, the degradation processes of products from the same population generally vary from each other due to various uncertainties. These two aspects bring great difficulty for ADT modeling. In this paper, we propose an improved ADT model considering both long-range dependence and unit-to-unit variability. To be specific, fractional Brownian motion (FBM) is utilized to capture the long-range dependence in the degradation process. The unit-to-unit variability among multiple products is captured by a random variable in the degradation rate function. To ensure the accuracy of the parameter estimations, a novel statistical inference method based on expectation maximization (EM) algorithm is proposed, in which the maximization of the overall likelihood function is achieved. The effectiveness of the proposed method is fully verified by a simulation case and a microwave case. The results show that the proposed model is more suitable for ADT modeling and analysis than existing ADT models.

翻译：加速退化试验是评估高可靠性产品可靠性与寿命的有效手段。现有研究表明，部分产品因与环境相互作用，其退化过程具有非马尔可夫性与长程依赖性。此外，由于各种不确定因素影响，同类产品的退化过程通常存在个体差异。这两个方面给加速退化试验建模带来了极大困难。本文提出一种改进的加速退化试验模型，同时考虑长程依赖与个体差异。具体而言，采用分数布朗运动描述退化过程中的长程依赖特征，并通过在退化速率函数中引入随机变量刻画多个产品间的个体差异。为确保参数估计精度，提出一种基于期望最大化算法的新型统计推断方法，实现了整体似然函数的最大化。通过仿真案例与微波器件案例充分验证了所提方法的有效性。结果表明，与现有加速退化试验模型相比，本文模型更适用于加速退化试验建模与分析。