We present a process monitoring scheme aimed at detecting changes in the networked structure of process data that is able to handle, simultaneously, three pervasive aspects of industrial systems: (i) their multivariate nature, with strong cross‐correlations linking the variables; (ii) the dynamic behavior of processes, as a consequence of the presence of inertial elements coupled with the high sampling rates of industrial acquisition systems; and (iii) the multiscale nature of systems, resulting from the superposition of multiple phenomena spanning different regions of the time‐frequency domain. Contrary to current approaches, the multivariate structure will be described through a local measure of association, the partial correlation, in order to improve the diagnosis features without compromising detection speed. It will also be used to infer the relevant causal structure active at each scale, providing a fine map for the complex behavior of the system. The scale‐dependent causal networks will be incorporated in multiscale monitoring through data‐driven sensitivity enhancing transformations (SETs). The results obtained demonstrate that the use of SET is a major factor in detecting process upsets. In fact, it was observed that even single‐scale monitoring methodologies can achieve comparable detection capabilities as their multiscale counterparts as long as a proper SET is employed. However, the multiscale approach still proved to be useful because it led to good results using a much simpler SET model of the system. Therefore, the application of wavelet transforms is advantageous for systems that are difficult to model, providing a good compromise between modeling complexity and monitoring performance. Copyright © 2015 John Wiley & Sons, Ltd.