Robust Multivariate Functional Control Charts

Profile monitoring assesses the stability over time of one or multiple functional quality characteristics to quickly detect special causes of variation that act on a process. 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. Because anomalous observations can seriously affect the monitoring performance, profile monitoring methods that are able to successfully deal with outliers are needed. To this aim, we propose a new framework, referred to as robust multivariate functional control charts (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 univariate filter to identify functional cellwise outliers to be replaced by missing components; (II) a robust 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 quantify the monitoring performance of the RoMFCC by comparing it with some competing methods already available 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.