Abstract

Statistical process monitoring of multichannel profiles presents a fundamental challenge: most existing methods target mean shifts and perform poorly when the process degrades through changes in the covariance structure. Yet covariance monitoring is inherently difficult. It demands estimating a large number of parameters that may shift in a subtle and sparse manner, with anomalies affecting only a small subset of cross-profile dependencies.
We introduce a new control chart that leverages functional graphical models to capture and monitor conditional dependencies between profiles in an interpretable way. Monitoring is performed through a nonparametric combination of likelihood-ratio tests across multiple sparsity levels, enabling the chart to detect both diffuse and highly localized covariance shifts without requiring prior knowledge of their structure. A key practical advantage is that the chart naturally pinpoints which between-profile relationships have likely shifted, with no additional computational overhead.
We evaluate the MPC chart through an extensive Monte Carlo simulation study against state-of-the-art competitors, demonstrating its superior sensitivity to sparse covariance changes. A case study on multichannel temperature profiles from an industrial roasting machine showcases its applicability in real manufacturing settings.

Acknowledgements

The research work of C. Capezza and D. Forcina was funded by the Department of Industrial Engineering, University of Naples Federico II within the project SMADI – Statistical Methods for Anomaly Detection in Industry 4.0. The research work of A. Lepore and B. Palumbo has been carried out within the framework of the INVITALIA R&D&I Project NEMESI “New Engineering \& Manufacturing Enhanced System Innovation”, CUP C67G22000420008.