Process curves are multi-variate finite time series data coming from manufacturing processes. This paper studies machine learning methods for drifts of process curves. A theoretic framework to synthetically generate process curves in a controlled way is introduced in order to benchmark machine learning algorithms for process drift detection. A evaluation score, called the temporal area under the curve, is introduced, which allows to quantify how well machine learning models unveil curves belonging to drift segments. Finally, a benchmark study comparing popular machine learning approaches on synthetic data generated with the introduced framework shown.