Multivariate degradation processes have been observed in many engineering systems. Most existing multivariate degradation modeling techniques, such as multivariate general path models or multivariate Wiener process models, assume an underlying Gaussian dependence structure. Unfortunately, in reality, the dependencies among degradation processes are often nonlinear, asymmetric and greatly tail-skewed, and thus limit the usefulness of the conventional modeling techniques in practice. To overcome these limitations, in this paper, we develop a copula-based multivariate modeling framework. Three fundamental copula classes are applied to model the complex dependence structure among correlated degradation processes. Statistical inference and model selection techniques, including two graphical diagnostic tools, a test of independence and a goodness-of-fit test, are employed to identify the best model. The advantages of the proposed modeling framework are demonstrated through simulation studies. And we also discuss the effect of ignoring tail dependence on system failure probability assessment. Finally, the applications of the copula-based multivariate degradation models on both system reliability evaluation and remaining useful life prediction are provided. The proposed methodology is illustrated using a numerical example.

在许多工程系统中已经观察到多变量降解过程。大多数现有的多元退化建模技术，例如多元通用路径模型或多元维纳过程模型，都假设有一个潜在的高斯依赖结构。不幸的是，在现实中，退化过程之间的依赖关系通常是非线性的、不对称的和严重的尾部偏斜，因此限制了传统建模技术在实践中的实用性。为了克服这些限制，在本文中，我们开发了一个基于 copula 的多元建模框架。应用三个基本的 copula 类来模拟相关退化过程之间的复杂依赖结构。统计推断和模型选择技术，包括两个图形诊断工具，采用独立性检验和拟合优度检验来确定最佳模型。通过仿真研究证明了所提出的建模框架的优点。我们还讨论了忽略尾部依赖对系统故障概率评估的影响。最后，提供了基于 copula 的多元退化模型在系统可靠性评估和剩余使用寿命预测中的应用。使用数值示例说明了所提出的方法。提供了基于 copula 的多元退化模型在系统可靠性评估和剩余使用寿命预测中的应用。使用数值示例说明了所提出的方法。提供了基于 copula 的多元退化模型在系统可靠性评估和剩余使用寿命预测中的应用。使用数值示例说明了所提出的方法。