The flight performance of a supersonic air-breathing missile is optimized with an automated loop taking into account design uncertainties through a statistical approach. Each characteristic of the missile (aerodynamic coefficient, inlet performance, mass) is altered with scale factors following a Gaussian distribution. A specific module performs statistical computations in order to predict the mean value and standard deviation of the performance. The optimization process is conducted only on the geometrical parameters of the inlet, which is one of the key elements of the aeropropulsive system. A representative mission is modelized leading to three performance objectives: the longitudinal acceleration factor after the boost phase, the maneuverability factor during counter-defense maneuvers and the fuel consumption during cruise.