In many modern industrial scenarios, the measurements of the quality characteristics of interest are often required to be represented as functional data or profiles. This motivates the growing interest in extending traditional univariate statistical process monitoring (SPM) schemes to the functional data setting. This article proposes a new SPM scheme, which is referred to as adaptive multivariate functional EWMA (AMFEWMA), to extend the well-known exponentially weighted moving average (EWMA) control chart from the univariate scalar to the multivariate functional setting. The favorable performance of the AMFEWMA control chart over existing methods is assessed via an extensive Monte Carlo simulation. Its practical applicability is demonstrated through a case study in the monitoring of the quality of a resistance spot welding process in the automotive industry through the online observations of dynamic resistance curves, which are associated with multiple spot welds on the same car body and recognized as the full technological signature of the process.

翻译：在许多现代工业场景中，感兴趣的质量特性测量值通常需要表示为函数型数据或轮廓曲线。这促使人们日益关注将传统单变量统计过程监控（SPM）方案扩展到函数型数据场景。本文提出了一种新的SPM方案，称为自适应多元函数EWMA（AMFEWMA），旨在将著名的指数加权移动平均（EWMA）控制图从单变量标量设置扩展到多元函数设置。通过广泛的蒙特卡洛模拟评估了AMFEWMA控制图相较于现有方法的优越性能。其实际适用性通过一个案例研究得到验证：该案例通过在线观测动态电阻曲线（该曲线与同一车身上的多个焊点相关联，并被视作该过程的完整技术特征）来监控汽车工业中电阻点焊过程的质量。