Real-Time Covariance Monitoring for Multichannel Profiles
摘要
This paper introduces a control chart designed to detect covariance shifts in multichannel profiles—a specific type of multivariate functional data characterized by multiple interdependent channels with shared structural patterns. Existing approaches primarily focus on monitoring the mean of profiles and often struggle with detecting complex covariance shifts due to high dimensionality and unknown shift patterns. To address this challenge, the proposed control chart combines several penalized likelihood ratio tests with different penalty parameters, enabling the effective identification of diverse covariance shifts. Covariance monitoring is reframed as a change detection problem in the precision matrix, leveraging functional graphical models to capture the conditional dependence structure among multichannel profiles. The effectiveness of the proposed method, along with its practical applicability, is demonstrated through a comparative study with state-of-the-art techniques in a real-world case study.