The quality characteristics in manufacturing processes are often represented in terms of spatially- or time-ordered data, called “profiles”, which are characterized by amplitude and phase variability. In this context, curve registration plays a key role, as it allows separating the two kinds of between-profiles variability and reducing any undesired inflation of the natural phase variability. In the mainstream literature, warping functions are not generally considered in the monitoring process, even though this may cause significant information loss. We propose a novel approach for profile monitoring that combines the functional principal component analysis and the use of parametric warping functions. The key idea is to jointly monitor the stability over time of the registered profiles (i.e., the information related to amplitude variability) and the registration coefficients (i.e., the information related to phase variability). This allows improving the capability of detecting unnatural pattern modifications, thanks to a better characterization of the overall natural variability. The benefits of a proper management of functional data registration, together with the advantages over the most common approaches used in the literature, are demonstrated by means of Monte Carlo simulations. The proposed methodology is finally applied to a real industrial case study relying on a dataset acquired in waterjet cutting processes under different health conditions of the machine tool.