This paper introduces a graph signal processing (GSP) framework for industrial process monitoring. Through a graph built to represent the variables of an industrial plant and their relationships, we show how to transform each sample vector observation using the graph Fourier transform (GFT) in order to infer the status of the plant. To validate the proposed method we compare it to the state of the art PCA T2 and Q methods for the Tennessee Eastman Process (TEP), a widely used benchmark for validation of methods in control and process monitoring. The results show our method outperforms PCA in most cases.