DOE (design of experiments) was applied to the design of a knuckle as a part of a suspension system. Specifically, knuckle made of aluminum alloy was optimized considering the strength. On the other hand, design variables were set as shape variables. During structural optimization using DOE, an orthogonal array strategy was developed to determine the optimum design. The relevant discrete variables were treated as levels. Since the conventional orthogonal array did not consider the constraint, however, the characteristic function was defined to include the effect of constraint feasibility. The general DOE was expanded to include problems with constraints related to the new characteristic function.