Random effects are ubiquitous in the degradation processes of multiple performance characteristics (PCs) of a complex system, and these PCs are not commonly independent. Neglecting either of the above features will lead to bias in system reliability estimation. Therefore, this study develops a reliability estimation method for the complex systems with multiple PC degradations considering both of the features. First, a Wiener process-based marginal degradation model with random effects (including the random initial PC, unit-to-unit variability, temporal uncertainty, and measurement errors) is proposed to track the degradation path of each PC. A model based on D-vine copulas is put forward to describe the correlation among multiple PCs. Then, a system reliability function is derived based on the two models. Furthermore, a two-step statistical inference is developed to estimate the unknown parameters in the system reliability function. Finally, using a practical case, the effectiveness of the proposed method is illustrated.

随机效应在复杂系统的多个性能特征（PC）的退化过程中无处不在，并且这些 PC 通常不是独立的。忽略上述任何一个特性都会导致系统可靠性估计出现偏差。因此，本研究开发了一种考虑这两个特征的具有多个 PC 退化的复杂系统的可靠性估计方法。首先，提出了一种基于 Wiener 过程的具有随机效应（包括随机初始 PC、单元间可变性、时间不确定性和测量误差）的边际退化模型来跟踪每个 PC 的退化路径。提出了一个基于D-vine copulas的模型来描述多个PC之间的相关性。然后，基于这两个模型推导出系统可靠性函数。此外，开发了两步统计推断来估计系统可靠性函数中的未知参数。最后，通过一个实际案例，说明了所提方法的有效性。