Degradation is an unavoidable phenomenon in industrial systems. Hidden Markov models (HMMs) have been used for degradation modeling. In particular, segmental HMMs have been developed to model the explicit relationship between degradation signals and hidden states. However, existing segmental HMMs deal only with univariate cases, whereas in real systems, signals from various sensors are collected simultaneously, which makes it necessary to adapt the segmental HMMs to deal with multivariate processes. Also, to make full use of the information from the sensors, it is important to differentiate stable signals from deteriorating ones, but there is no good way for this, especially in multivariate processes. In this paper, the multivariate exponentially weighted moving average (MEWMA) control chart is employed to identify deteriorating multivariate signals. Specifically, the MEWMA statistic is used as a comprehensive indicator for differentiating multivariate observations. Likelihood Maximization is used to estimate the model parameters. To avoid underflow, the forward and backward probabilities are normalized. In order to assess degradation, joint probabilities are defined and derived. Further, the occurrence probability of each degradation state at the current time, as well as in the future, is derived. The Commercial Modular Aero-Propulsion System Simulation (C-MAPSS) dataset of NASA is employed for comparative analysis. In terms of degradation assessment and prediction, the proposed model performs very well in general. By sensitivity analysis, we show that in order to improve further the performance of the method, the weight of the chart should be set relatively small, whereas the method is not sensitive to the change of the in-control average run length (ARL).

降解是工业系统中不可避免的现象。隐马尔可夫模型（HMM）已用于降级建模。特别是，已经开发了分段HMM，以对降级信号和隐藏状态之间的显式关系进行建模。但是，现有的分段HMM仅处理单变量情况，而在实际系统中，同时收集来自各种传感器的信号，这使得有必要使分段HMM适应多变量过程。同样，要充分利用传感器的信息，将稳定信号与恶化信号区分开也很重要，但这没有好的方法，尤其是在多变量过程中。在本文中，多元指数加权移动平均值（MEWMA）控制图用于识别恶化的多元信号。具体而言，MEWMA统计信息用作区分多元观察结果的综合指标。似然最大化用于估计模型参数。为了避免下溢，将前向概率和后向概率标准化。为了评估退化，定义并导出联合概率。此外，导出当前以及将来每个劣化状态的发生概率。NASA的商业模块化航空推进系统仿真（C-MAPSS）数据集用于比较分析。在退化评估和预测方面，所提出的模型总体上表现良好。通过敏感性分析，