In machining process planning, it is critical to ensure that the part created following the manufacturing steps complies with the designated design tolerances. However, the challenge is that manufacturing errors are stochastic in nature and are introduced at almost every step of executing a plan, for example, due to inaccuracy of tooling, misalignment of location, etc. Furthermore, these errors accumulate or “stack up” as the machining process progresses to inevitably produce a part that varies from the original design. The resulting variations should be within prescribed design tolerances for the manufactured part to be acceptable. In this work, we present a novel approach for assessing the manufacturing errors by representing variations of nominal features with transformations that are defined in terms of extents of the features' degrees-of-freedom (DOFs) within their design and manufacturing tolerance zones (MTZs). We show how the manufacturing errors stackup can be effectively represented by the composition and intersection of these transformations. Several examples representing scenarios of different complexities are demonstrated to show the applicability of our approach in assessing the influence of manufacturing errors on the design tolerances following a machining plan. Discussions of our approach are provided to address concerns with the accuracy and efficiency as well as to disclose the potential of our approach to enable a tolerance-aware process planning system.