Modeling correlated non-normal contributors in geometric stack-up analysis

This work presents a computational framework for tolerance chain analysis based on multivariate statistical modelling accommodating both prescribed moments and correlations. The proposed method generates multivariate datasets matching either measured or proposed component characteristics, enabling realistic statistical virtual assembly. By using a transformed multi-variate Normal distribution, it is possible to represent the mean, variance, skewness, kurtosis, and covariance structure of the real parts' geometric variability. This allows tolerance propagation analysis that reflects actual manufacturing variability. Applications include predictive assembly simulations, functional tolerance optimization, and data-driven design verification in industrial contexts.