The objective of this study was to demonstrate the use of stochastic expansions in the quantification of margins and uncertainties in complex aerospace systems. In this study, stochastic expansions, based on nonintrusive polynomial chaos, were utilized for efficient representation of uncertainty both in design metrics and associated performance limits of a system. Additionally, procedures were outlined for analyzing systems that contain different uncertainty types between the performance metrics and performance limits. These methodologies were demonstrated on three model problems, each possessing mixed (epistemic and aleatory) uncertainty, which was propagated through the models using second-order probability. The first was a complex system of highly nonlinear analytical functions. The second was a multisystem, physics based model for spacecraft reentry. The performance metrics consisted of two systems used to determine the maximum g-load, the necessary bank angle correction, and maximum convective heat load along a reentry trajectory. The last model was a multidisciplinary model for the design and analysis of a High Speed Civil Transport. Overall, the methodologies and examples of this work have detailed an approach for measuring the reliability of complex aerospace systems as well as the importance of quantifying margins and uncertainties for the design of reliable systems.