In this paper we present a framework for addressing a variety of engineering design challenges with limited empirical data and partial information. This framework includes guidance on the characterisation of a mixture of uncertainties, efficient methodologies to integrate data into design decisions, and to conduct reliability analysis, and risk/reliability-based design optimisation. To demonstrate its efficacy, the framework has been applied to the NASA 2020 uncertainty quantification challenge. The results and discussion in the paper are with respect to this application.