In the practical design process, uncertainty in the parameters should be appropriately taken into account. For example, earthquakes should be considered as uncertain phenomena. Robust design method is known as an effective design method under such uncertain-ties, where a design is found to be insensitive to environment and other uncontrollable factors. Worst-case design of structures is a populism approach as a robust design method, where the objective function and/or the constraints are assigned to the worst values of the structural responses. However, predicting the exact extremes from small samples is difficult in general. Hence, we have proposed use of the k-th worst value instead of the exact worst value. We can predict and control more accurately the behavior of RS by this approach. We could successfully apply the approach to seismic design problems linking with a prescribed accuracy. Through a numerical example, we show the decision based on the k-th order statistics is closely related to the reliability index under some assumptions. The result indicates a new aspect of the proposed robust design method.