An adaptive multivariate functional EWMA control chart

In many modern industrial scenarios, 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 proposed method distinguishes itself by adaptively selecting the weighting parameter in the calculation of the EWMA statistic to enhance the sensitivity of the AMFEWMA control chart across a spectrum of potential out-of-control scenarios. Such adaptability is essential in industrial processes, where multivariate functional quality characteristics are also subject to varying degrees of change. 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 monitoring the quality of a resistance spot welding (RSW) process in the automotive industry through online observations of dynamic resistance curves, which are associated with multiple spot welds on the same car body and are recognized as highly representative of the RSW process quality. The proposed method is implemented in the R package funcharts, available online on CRAN.