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Concurrent monitoring schemes that achieve simultaneous process and quality-relevant monitoring have recently attracted much attention. In this Article, we formulate a supervised fault diagnosis framework based on canonical correlation analysis (CCA) with regularization, which includes quality-relevant and quality-irrelevant fault diagnosis. Monitoring indices based on regularized concurrent CCA models are introduced to perform quality-relevant, potentially quality-relevant, and quality-irrelevant monitoring. Additionally, contribution plots and generalized reconstruction-based contribution methods are developed, along with their implications for the diagnosis based on the various monitoring indices. Finally, the Tennessee Eastman process is used to illustrate the supervised monitoring and diagnosis of quality-relevant and quality-irrelevant disturbances, and the 15 known disturbances are classified into two categories based on whether they have an impact on product quality variables.