A computer aided tolerance analysis tool is presented that assists the designer in evaluating worst case quality of assembly after tolerances have been specified. In tolerance analysis calculations, sets of equations are generated. The number of equations can be restricted by using a minimum number of points in which quality of assembly is calculated. The number of points needed depends on the type of surface association. The number of parameters in the set of equations can be reduced by considering the most critical direction for the assembly condition. The latter direction, called virtual plan fragment direction, is determined using a virtual plan fragment table, based on an analogy to the plan fragment table used in degrees of freedom (DOF) analysis. This reduced set of equations is then solved and optimized in order to find the maximum/minimum values for the assembly condition using simulated annealing. This method for tolerance analysis has been implemented in a feature based (re-Idesign support system called FROOM, as part of the functional tolerancing module.