The mounting increase in the technological complexity of modern engineering systems requires compound uncertainty quantification, from a quantitative and qualitative perspective. This paper presents a Compound Uncertainty Quantification and Aggregation (CUQA) framework to determine compound outputs along with a determination of the greatest uncertainty contribution via global sensitivity analysis. This was validated in two case studies: a bespoke heat exchanger test rig and a simulated turbofan engine. The results demonstrated the effective measurement of compound uncertainty and the individual impact on system reliability. Further work will derive methods to predict uncertainty in-service and the incorporation of the framework with more complex case studies.