Precisely assessing the reliability of adhesive bonds is crucial for both ensuring structural safety and reducing mass. Classical design and dimensioning methods often rely on fixed, empirically derived safety margins combined with deterministic models, which can lead to overly conservative and inefficient designs. Models based on modern crack initiation theories, such as finite fracture mechanics, offer a physics-based approach to understand the effect of uncertainties. In this study we make use of a highly efficient finite fracture mechanics solution for the analysis of adhesive joints with brittle, structural adhesives to study the effect of a large set of geometrical and material properties as well as geometrical nonlinearity and thermal residual stresses. The model allows the quantification of uncertainties stemming from variability in input parameters using probabilistic approaches. By defining survival probabilities, the results are related to conventional safety factor methods, providing insights into the limitations of empirical approaches. Furthermore, we analyze the effect of thermal eigenstrains on the nonlinear fracture analysis and make use of a clustering of individual uncertainties to discuss partial safety factors.