The application of the concept of robust design, based on Taguchi's design philosophy, in formulating and solving large, computationally intensive, nonlinear optimization problems whose analysis is based on a linear system of equations is investigated. The design problem is formulated using a robust optimization procedure that utilizes the expected value of Taguchi's loss function as the objective. An efficient solution scheme that uses approximate expressions for the gradients and employs a fast reanalysis technique for their evaluation is introduced. This approach is validated by solving a simple minimum cost welded beam design problem; where the dimensions of the weldment and the beam are found without exceeding the limitations stated on the shear stress in the weld, normal stress in the beam, buckling load on the beam and tip deflection of the beam. The method is then used to obtain the optimal shape of an engine connecting rod, that minimizes its weight when subject to geometric constraints on the shape variables, and behavioral constraints such as stress and buckling loads. The results obtained by solving the conventional and robust formulations of this problem, and the considerable savings in time that result by virtue of using the fast reanalysis technique are presented. The methodology presented in this work is expected to be useful in reducing the computational effort in obtaining insensitive designs of large structures and machines.