A method to identify robust designs of mechanical parts with free-form shapes is proposed. For each design, the geometry and operating conditions represent one design point in the design space, with noise altering the design point leading to a change in performance. A shape optimization process is conducted for each example problem. Each successive iteration during the process produces an iterative design point with the final one being the optimum design. Once the process is completed, a design of experiment approach is used to apply noise in order to generate samples around each and every iterative design point. Then a simple statistical method is utilized to analyze the samples in order to evaluate the robustness of each iterative design. The results show that an optimum design is not necessarily robust.