Abstract: The assembly dimension chain serves as the foundation for tolerance allocation in CNC machine tools, under operational conditions, variations in assembly dimension chains are observed, with their magnitude typically exceeding tolerance values by a significant margin. Consequently, the error accumulation relationships reflected by conventional assembly dimension chains are rendered inaccurate. A variant assembly dimension chain accounting for machine tool service conditions was developed in this study. Specifically, a mathematical model with machine tool travel as the independent variable was established for geometric tolerance analysis. Based on this framework, a variant assembly dimension chain characterizing the parallelism between the spindle axis and Z-axis motion was formulated. The component loop exhibiting the most significant influence on the closed loop was identified. To mitigate positional deviations of tolerance zones induced by gravitational loads, an active precision design methodology for the guide rail positioning reference surface was implemented. This approach has been demonstrated to enhance straightness accuracy of the horizontal axis motion in beams/gantry-type columns.