The tolerance analysis of an assembly is an important issue for mechanical design. Among many tolerance analysis methods, the conventional statistical tolerance analysis method is the most popular one. However, the conventional statistical tolerance analysis method is based on the normal distribution. It fails to predict the resultant tolerance of an assembly with features in non-normal distributions. In this paper, the distributions of features are transferred into statistical moments first. Then, the tolerance stack-up can be handled based on these moments. Finally, the computed resultant moments can be mapped back to probability distribution to find the resultant tolerance specification of the assembly. Two examples are used to demonstrate the proposed method. Compared to the resultants by Monte Carlo simulation with 1,000,000 samples, the predicted resultant tolerance specifications by this method are only −0.868% and 0.799% differences. The predicted resultant tolerances of this method are fast and accurate.

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