This paper presents a framework to support decision-making in aircraft conceptual design optimisation under uncertainty. Emphasis is given to graphical visualisation methods capable of providing holistic yet intuitive relationships between design, objectives, feasibility and uncertainty spaces. Two concepts are introduced to allow interactive exploration of the effects of (1) target probability of constraint satisfaction (price of feasibility robustness) and (2) uncertainty reduction through increased state-of-knowledge (cost of uncertainty) on design and objective spaces. These processes are tailored to handle multi-objective optimisation problems and leverage visualisation techniques for dynamic inter-space mapping. An information reuse strategy is presented to enable obtaining multiple robust Pareto sets at an affordable computational cost. A case study demonstrates how the presented framework addresses some of the challenges and opportunities regarding the adoption of Uncertainty-based Multidisciplinary Design Optimisation (UMDO) in the aerospace industry, such as design margins policy, systematic and conscious definition of target robustness and uncertainty reduction experiments selection and prioritisation.