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.