Most statistical process monitoring methods for multichannel profiles focus solely on the mean and are almost ineffective when changes involve the covariance structure. Although it is known to be crucial, covariance monitoring requires estimating a much larger number of parameters, which may shift in a subtle and sparse fashion. That is, an out-of-control (OC) state may manifest with small deviations and affect only a very limited subset of these parameters. To address these difficulties, we propose a multichannel profile covariance (MPC) control chart based on functional graphical models that provide an interpretable representation of conditional dependencies between profiles. A nonparametric combination of the likelihood-ratio tests corresponding to different sparsity levels is then used to draw an overall inference and signal whether an OC state may have occurred. Between-profile relationships that are likely to have shifted are naturally identified at no additional computational cost. An extensive Monte Carlo simulation study compares the MPC control chart with state-of-the-art competitors, and a case study on monitoring multichannel temperature profiles in a roasting machine illustrates its practical applicability.

翻译：大多数多通道轮廓的统计过程监控方法仅关注均值，当变化涉及协方差结构时几乎无效。尽管协方差监控至关重要，但其需要估计远更多参数，这些参数可能以微妙且稀疏的方式发生偏移。即，失控状态可能表现为微小偏差，且仅影响这些参数中非常有限的子集。为解决这些困难，我们提出一种基于功能图模型的多通道轮廓协方差控制图，该模型提供了轮廓间条件依赖关系的可解释表示。随后，通过结合对应不同稀疏水平的似然比检验进行非参数组合，以得出整体推断并指示失控状态是否可能发生。可能发生偏移的轮廓间关系可在无需额外计算成本的情况下自然识别。一项广泛的蒙特卡洛模拟研究将MPC控制图与先进竞争方法进行比较，而关于烘焙机多通道温度轮廓监控的案例研究则说明了其实际适用性。