This paper presents a two-stage Machine Learning (ML) model to predict the arrival time of In-Process Control (IPC) samples at the quality testing laboratories of a chemical company. The model was developed using three iterations of the CRoss-Industry Standard Process for Data Mining (CRISP-DM) methodology, each focusing on a different regression approach. To reduce the ML analyst effort, an Automated Machine Learning (AutoML) was adopted during the modeling stage of CRISP-DM. The AutoML was set to select the best among six distinct state-of-the-art regression algorithms. Using recent real-world data, the three main regression approaches were compared, showing that the proposed two-stage ML model is competitive and provides interesting predictions to support the laboratory management decisions (e.g., preparation of testing instruments). In particular, the proposed method can accurately predict 70% of the examples under a tolerance of 4 time units.