In modern Industry 4.0 applications, a huge amount of data is acquired during manufacturing processes that are often contaminated with anomalous observations in the form of both casewise and cellwise outliers. These can seriously reduce the performance of control charting procedures, especially in complex and high-dimensional settings. To mitigate this issue in the context of profile monitoring, we propose a new framework, referred to as robust multivariate functional control chart (RoMFCC), that is able to monitor multivariate functional data while being robust to both functional casewise and cellwise outliers. The RoMFCC relies on four main elements: (I) a functional univariate filter to identify functional cellwise outliers to be replaced by missing components; (II) a robust multivariate functional data imputation method of missing values; (III) a casewise robust dimensionality reduction; (IV) a monitoring strategy for the multivariate functional quality characteristic. An extensive Monte Carlo simulation study is performed to compare the RoMFCC with competing monitoring schemes already appeared in the literature. Finally, a motivating real-case study is presented where the proposed framework is used to monitor a resistance spot welding process in the automotive industry.

翻译：在现代工业4.0应用中，制造过程中采集的海量数据常因个案异常值和变量异常值两种形式的异常观测而受污染，这严重降低了控制图程序的性能，尤其在复杂高维场景下。为缓解轮廓监测中的这一问题，我们提出了一种名为鲁棒多元函数控制图（RoMFCC）的新框架，该框架既能监测多元函数数据，又对函数型个案异常值和变量异常值具有鲁棒性。RoMFCC依赖四个核心要素：（I）函数型单变量滤波器——识别函数型变量异常值并将其替换为缺失成分；（II）鲁棒多元函数缺失值插补方法；（III）个案鲁棒降维；（IV）多元函数质量特性的监测策略。通过大规模蒙特卡洛仿真研究，将RoMFCC与已有文献中的竞争监测方案进行比较。最后，展示了一个激励性的实际案例研究，该案例将所提框架应用于汽车行业的电阻点焊过程监测。