A sensitivity analysis of a supersonic intake of a turbine-based combined cycle (TBCC) engine is presented. A multi-block Reynolds-averaged Navier-Stokes (RANS) solver was used to compute the flowfield. While RANS simulation provides more realistic performance estimate than a simplified cycle analysis, the intake design must also take into account in-flight uncertainties for robustness. In this study, we focus on the effect of geometric uncertainties on the intake performance, and propose a practical approach to simulation-based sensitivity analysis. The method begins by constructing a radial-basis function (RBF) network, trained via efficiently sampled simulations. Using the RBF network as the surrogate model, sensitivity analysis is performed using the analysis of variance (ANOVA) technique. This approach makes it possible to perform a generalised multi-input-multi-output sensitivity analysis based on high-fidelity simulation. The resulting sensitivity indices help identify dominant parameters as well as the interaction among multiple parameters, which can then be used for design refinement.