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Abstract Aerospace composites assemblies/joining demand ultra-high precision due to critical safety requirements, which necessitate adherence to indicators of risk that are often difficult to quantify. This study examines one important indicator, the residual stress that arises as a result of dimensional mismatch between mating components during the composite structures assembly process. Conventional simulations of large components assemblies investigated the process at a local or global scale, but lacked detailed exploitation of multi-layer stress analysis at integrated scale for composite structures. We develop a novel digital twin simulation for joining large composite structures with mechanical fasteners. The digital twin simulation integrates global features and local features for detailed investigation of stresses. We perform a statistical analysis to better understand the numerical properties of residual stresses after the fastening. Goodness-of-Fit tests and normality tests are used to explore the probabilistic distributions of the stresses exceeding a chosen safety threshold. The case study is conducted based on composite fuselage joining. The results show the stresses in composite structures assembly follow extreme value distributions (such as Weibull, Gumbel) rather than the widely used Gaussian distribution. The stresses in joined composite structures differ across layers, which can be attributed to the anisotropic material behavior.