Although many kernel-based quality-related monitoring methods have been developed for nonlinear processes, the nonlinearity between process variables and quality indicators is not well interpreted by kernel mapping and subsequent regression. To monitor a nonlinear quality-related latent space, a novel framework that consists of quality-related and process-related statistics rather than quality-related and quality-independent statistics is proposed. First, we train a quality-driven autoencoder (QdAE) with least-squares regularization through the gradient descent algorithm using quality indicators Quality-related information can be predicted using latent variables through the auxiliary supervision of the quality indicators. Second, quality-related statistic T-y(2) is constructed to monitor the quality indicators. In the residual subspace derived by the QdAE, we compute the SPE statistic, which contains quality-related and quality-independent information. Furthermore, we present a strategy to enhance the SPE statistic to improve performance. Considering the quality-related and process-related monitoring using T-y(2) and SPEnew, we can also provide a reliable decision about whether the fault is quality-related or quality-independent. Finally, the proposed method is evaluated using the cases in the Tennessee Eastman process.