To make informed decisions during the concept selection activities of a fusion power plant it is necessary to evaluate the impact of uncertainties on the feasibility and performance of each concept. A framework for uncertainty quantification and sensitivity analysis has been developed for the PROCESS systems code to allow the direct comparison of different DEMO concepts. To account for epistemic uncertainty, the uncertainty quantification was based on interval analysis, where only the bounds of the interval have to be assumed for each uncertain parameter, and the uncertainty was propagated with Monte Carlo and Latin Hypercube Sampling. The sensitivity analysis was based on the pinching method, consisting in reducing the interval uncertainty of each input parameter to a baseline point one by one, and measuring the uncertainty reduction in the output interval. Its application is shown using the European H-mode DEMO baseline as a use case. Results suggest that the thermal He-4 fraction in plasma, plasma elongation, and H-factor should be examined further to reduce risks on its feasibility.