This paper deals with the ship design support system in consideration of the accuracies of the analyses. When the error margin is included in an analysis, the boundary of design variables becomes indistinct. This area is called "Gray Zone". In this paper, input and output information of analyses are expressed by expected value and standard deviation, and the deterioration of objective function caused by "Gray zone" is calculated by repeating the robustness optimization. As a result, influences of the accuracies of the analyses on objective function are quantitatively understood. Some examples are shown at the end of this paper.