An efficient, robust design optimization method based on surrogate models was developed and applied to a practical design problem of a low-noise, coaxial contrarotating rotor. A classical Monte Carlo simulation was carried out at greatly reduced computational cost through dual-level Kriging surrogate models, and it determines the variance of the simulation for uncertainty quantification. The accuracy and numerical stability of the Kriging model were improved by a mathematical indicator of the function trend. The numerical instabilities of the Kriging model in finding distribution parameters were also reduced by the approaches of penalization and cross-validation in a maximum likelihood evaluation. Finally, the robust design optimization framework was applied to a low-noise DLR, German Aerospace Center contrarotating open rotor at a nominal takeoff condition. The objective function was to minimize an overall sound power level at the baseline thrust level. An efficient computational-fluid-dynamics approach of the harmonic balance method solved unsteady open-rotor flows, and aeroacoustic characteristics were computed by Ffowcs-Williams-Hawkings equations. The design variables were the radii of the front and aft rotors, rotor spacing, and pitch angle of the aft rotor. Aleatory uncertainties were considered in both geometric design variables and the freestream Mach number. Noise reduction of 3.3dB was achieved with reduced variance.