A reasonable description of the degradation process is essential for credible reliability assessment in accelerated degradation testing. Existing methods usually use Markovian stochastic processes to describe the degradation process. However, degradation processes of some products are non-Markovian due to the interaction with environments. Misinterpretation of the degradation pattern may lead to biased reliability evaluations. Besides, owing to the differences in materials and manufacturing processes, products from the same population exhibit diverse degradation paths, further increasing the difficulty of accurately reliability estimation. To address the above issues, this paper proposes an accelerated degradation model incorporating memory effects and unit-to-unit variability. The memory effect in the degradation process is captured by the fractional Brownian motion, which reflects the non-Markovian characteristic of degradation. The unit-to-unit variability is considered in the acceleration model to describe diverse degradation paths. Then, lifetime and reliability under normal operating conditions are presented. Furthermore, to give an accurate estimation of the memory effect, a new statistical analysis method based on the expectation maximization algorithm is devised. The effectiveness of the proposed method is verified by a simulation case and a real-world tuner reliability analysis case. The simulation case shows that the estimation of the memory effect obtained by the proposed statistical analysis method is much more accurate than the traditional one. Moreover, ignoring unit-to-unit variability can lead to a highly biased estimation of the memory effect and reliability.

翻译：在加速退化试验中，对退化过程的合理描述是进行可信可靠性评估的基础。现有方法通常采用马尔可夫随机过程来描述退化过程。然而，由于与环境的相互作用，某些产品的退化过程具有非马尔可夫性。对退化模式的误判可能导致可靠性评估产生偏差。此外，由于材料与制造工艺的差异，同一批次的产品会呈现出多样化的退化轨迹，这进一步增加了准确进行可靠性估计的难度。为解决上述问题，本文提出了一种融合记忆效应与个体差异的加速退化模型。退化过程中的记忆效应通过分数布朗运动捕捉，这反映了退化的非马尔可夫特性。个体差异在加速模型中被考虑，以描述多样化的退化轨迹。随后，给出了正常工况下的寿命与可靠性。此外，为准确估计记忆效应，设计了一种基于期望最大化算法的新统计分析方法。通过一个仿真案例和一个实际的调谐器可靠性分析案例，验证了所提方法的有效性。仿真案例表明，所提统计分析方法获得的记忆效应估计值比传统方法准确得多。此外，忽略个体差异会导致对记忆效应和可靠性的估计产生严重偏差。