In the robust shape optimization context, the evaluation cost of numerical models is reduced by the use of a response surface. Multi-objective methodologies for robust optimization that consist in simultaneously minimizing the function and a robustness criterion (the second moment) have already been developed. However, efficient estimation of the robustness criterion in the framework of time-consuming simulation has not been greatly explored. A robust optimization procedure based 15 on the prediction of the function and its derivatives by kriging is proposed. The second moment is replaced by an approximated version using Taylor expansion. A Pareto front is generated by a genetic algorithm named NSGA-II with a reasonable time of calculation. Seven relevant strategies are detailed and compared with the same calculation time in two test functions (2D and 6D). In each case, we compare the results when the derivatives are observed and 20 when they are not. The procedure is also applied to an industrial case study where the objective is to optimize the shape of a motor fan.