Purpose - To present a robust optimal design technique in the presence of system parameters uncertainties. Design/methodology/approach - The properties of normally distributed random variables are exploited, together with surface response fitting techniques, with the aim to reduce the computational cost in assessing the effect of uncertainties. Findings - A fast approximate method for computing statistical average is presented together with its implementation for the design of magnets for magnetic resonance imaging. Research limitations/implications - Future research will be focused to multi-dimensional problems and to the best choose of closed form expressions to evaluate statistical moments fitting. Practical implications - Robust optimal design methodologies are receiving an increasing interest in both academic and industrial research, due to their capability of coping with construction uncertainties and tolerances. Originality/value - The effectiveness of the simplified method has been demonstrated for an analytical example and on a simplified superconducting magnet design. The proposed strategy is quite general and it can be applied to a wide class of optimal design problems.