Abstract: Tolerance analysis is employed to analyze the tolerance accumulation relationship between the tolerances of component rings and the tolerance of the closed ring, with its core lying in the establishment of error accumulation relationships between components. The geometric features of components are treated as ideal straight lines or planes in current tolerance analysis methods, thus making it impossible to account for changes in the error accumulation relationships between components throughout the full stroke of machine tools. In response to this, a dimensional relationship model is proposed in this paper, where the geometric features of machine tool components are discretely represented as sets of discrete coordinate points. Under service conditions, components undergo deformation, and changes in the corresponding discrete points lead to the unclosure of dimensional chains. Here, an equivalent coplanar datum plane determined by three highest points is used to approximately replace the installation datum plane, ensuring the closure of dimensional chains and thereby establishing the error accumulation relationships between components under service conditions. On this basis, verification experiments on a horizontal machining center are conducted to validate the correctness of the dimensional relationship model under service conditions. After the dimensional relationship model under service conditions is established, reasonable allocation of component tolerances can be achieved by considering random errors, and active precision design of components can be realized by considering systematic errors.