The product is more complicated and the parts can fit to the adjacent parts with multiple constraints for improving the stiffness and accuracy of the assembly. The average dimension of the parts may shifts or drifts from the nominal value during the manufacturing process. And, the dimension distribution of the parts can be in different non- normal distribution since they are manufactured by different manufacture process. This method predicts more accurate resultants by an interpolation method. With this method, the assembled state of an assembly with multiple constraints can be evaluated. The assembly behaves a higher probability of stiffness, as if the minimum gap index is smaller. For the mean shift studied for the cases represented in this paper, the results show the difference between this model and the Monte Carlo method with 1,000,000 simulation samples is less than 0.5%. The two stack-up examples described in this paper show the predicted errors only 0.799% and -1.76% respectively. The proposed model is fast and accurate for non-normal distribution and process with mean shift or drift.