When a new product is designed in an industrial context, it must be possible to produce this product with the desired level of quality and at an acceptable cost for the market. One of the important quality criteria is compliance with functional tolerances. To evaluate the impact of manufacturing defects on the quality of parts produced, designers simulate the influence of the error stack-up in different machining operations to check compliance with functional tolerances. This paper builds on the model of manufactured part and the Jacobian–Torsor model and presents a combined approach for analyzing machined part tolerance taking into account the geometrical defects occurring in a multistage machining process (positioning defects and machining defects). This combined approach aims to help designers when evaluating the different process plans by predicting the worst quality of finished parts. This study uses interval arithmetic because it offers the advantage of expressing uncertainties and deviations.