This paper proposes a control chart for detecting covariance shifts in multichannel profiles, which are a specific type of multivariate functional data characterized by multiple interdependent channels with shared structural patterns. Such profiles are common in modern industrial systems, where monitoring covariance is critical for ensuring product quality and process stability. Existing methods focus primarily on monitoring mean profiles but often struggle with detecting complex covariance shifts due to the high dimensionality and unknown shift patterns. The proposed control chart leverages penalized likelihood ratio tests with varying penalty parameters to effectively identify diverse covariance shift patterns. Covariance monitoring is recast as detecting changes in a precision matrix by representing the conditional dependence structure among multichannel profiles through functional graphical models. The superior performance of the proposed control chart compared to state-of-the-art approaches and its practical applicability are illustrated through a simulation study and a case study.

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Monitoring the Covariance of Multichannel Profiles

  • Christian Capezza,
  • Davide Forcina,
  • Antonio Lepore,
  • Biagio Palumbo

摘要

This paper proposes a control chart for detecting covariance shifts in multichannel profiles, which are a specific type of multivariate functional data characterized by multiple interdependent channels with shared structural patterns. Such profiles are common in modern industrial systems, where monitoring covariance is critical for ensuring product quality and process stability. Existing methods focus primarily on monitoring mean profiles but often struggle with detecting complex covariance shifts due to the high dimensionality and unknown shift patterns. The proposed control chart leverages penalized likelihood ratio tests with varying penalty parameters to effectively identify diverse covariance shift patterns. Covariance monitoring is recast as detecting changes in a precision matrix by representing the conditional dependence structure among multichannel profiles through functional graphical models. The superior performance of the proposed control chart compared to state-of-the-art approaches and its practical applicability are illustrated through a simulation study and a case study.