Robust Multivariate Functional Control Chart

In modern Industry 4.0 applications, a huge amount of data is acquired during manufacturing processes and is often contaminated with outliers, which can seriously reduce the performance of control charting procedures, especially in complex and high-dimensional settings. In the context of profile monitoring, we propose a new framework that is referred to as robust multivariate functional control chart (RoMFCC) to monitor a multivariate functional quality characteristic while being robust to both functional casewise and componentwise outliers. In the former case, observations of the quality characteristic are contaminated in all functional variables or components, while, in the latter, the contamination affects one or more components independently. The RoMFCC relies on (I) a functional filter to identify componentwise outliers to be replaced by missing components; (II) a robust multivariate functional data imputation method; (III) a casewise robust dimensionality reduction; (IV) a monitoring strategy for the quality characteristic. Through a Monte Carlo simulation study, the RoMFCC is compared with competing schemes that have already appeared in the literature. A case study is finally presented where the proposed framework is used to monitor a resistance spot welding process in the automotive industry. RoMFCC is implemented in the R package funcharts, available online on CRAN.