The performance of high-quality products should be insensitive to environmental disturbances. Traditional design attempts to create quality in design by tightening manufacturing tolerances, which leads to high manufacturing cost. In spite of the apparent high-quality, when environmental variations appear, performance of products can be degraded. A robust design methodology is presented in this research, to produce a high-quality and low-cost product. By considering manufacturing tolerances and environmental disturbances early in the design stage, a robust design can be obtained. Because robust design requirements that involve first-order sensitivity are formulated as an optimization problem, to accurately evaluate gradients of constraints, a reliable second-order shape design sensitivity analysis (DSA) method is used.