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Title: Robust control charts for multivariate functional data Authors:  Christian Capezza - University of Naples Federico II (Italy) [presenting]
Fabio Centofanti - University of Naples Federico II (Italy)
Antonio Lepore - Universita di Napoli Federico II (Italy)
Biagio Palumbo - University of Naples Federico II (Italy)
Abstract: Profile monitoring evaluates the stability of a functional quality characteristic over time in order to identify special causes of variation that affect a process. Modern manufacturing processes in Industry 4.0 applications allow for acquiring large amounts of profile data, which, however, are frequently contaminated by anomalous observations in the form of both casewise and cellwise outliers. Then, profile monitoring techniques need to cope with outliers since they can significantly influence the monitoring performance. To achieve this, we propose a novel framework, referred to as a robust multivariate functional control chart (RoMFCC), which can monitor multivariate functional data while being robust to both functional casewise and cellwise outliers. The RoMFCC relies on four key components: (I) a univariate filter to find functional cellwise outliers that are replaced by missing components; (II) a robust functional data imputation method for missing values; (III) a casewise robust dimensionality reduction; and (IV) a monitoring strategy for the multivariate functional quality characteristic. To compare the RoMFCC with other competing methods in the literature, a thorough Monte Carlo simulation analysis is conducted to assess the monitoring performance of the RoMFCC. The proposed framework is then applied to monitor a resistance spot welding process in the automotive industry in a motivating real-case study.