Efficient statistical analysis of geometric tolerances using unified error distribution and an analytical variation model

Inaccuracies in conventional tolerance characterization methods, which are based on worst-case and root-square-error methods, as well as inefficiencies in Monte Carlo computational methods of statistical tolerance analysis, require an accurate and efficient method of statistical analysis of geometric tolerances. Here, we describe a unified error distribution model for various types of geometric tolerance to obtain the distribution of the deviations in different directions. The displacement distributions of planes, straight lines, and points are analyzed based on distributions within tolerance zones. The distribution of the displacements of clearance fits is then determined according to the precedence of the assembly constraints. We consider the accumulated assembly variations and displacement distributions, and an analytical model is constructed to calculate the distribution of the deviations of the control points and the process capability index to validate the functional requirements. The efficiency of the method is shown by applying it to the assembly of a single-rod piston cylinder. The results are compared with other statistical methods of tolerance analysis. We find an improvement of approximately 20 % in tolerance analysis, and the process capability index of the assembly procedure was reduced by 10 %.