In modern industrial processes, quality-relevant process monitoring methods are important to timely indicate abnormal product quality. Moreover, advanced closed-loop control systems have been widely applied to ensure consistent product quality. The process variations under closed-loop systems are obviously different from that of open-loop systems. The dynamics caused by feedback control brings challenges for quality-relevant process monitoring issue which has rarely been addressed before. Considering slowness is a good indicator of dynamics, a comprehensive decomposition of process variation is proposed with dual consideration of product quality and slowness. First, quality-relevant process variations are separated from process-relevant variations by maximizing correlation between latent variables and product quality meanwhile minimizing the slowness of latent variables. Both variations are further divided into static and dynamic subspaces with respect to temporal information. Thus, total process variations are decomposed into three subspaces, in which each one has a specific meaning. On the basis of this, the proposed method possesses the ability in simultaneously evaluating the influences on product quality and process dynamics which thus provides a fine-scale monitoring of process status. Finally, the efficacy of the proposed method is illustrated through a benchmark case and an industrial process, which are both under closed-loop control. (C) 2019 Elsevier Ltd. All rights reserved.