A low-cost approach for experimenting using numerical methods, including finite element analysis (FEA), is presented. The method is illustrated by its application to the design of a D-shaped shaft. A reduction of >23% in stress is achieved compared with an “educated guess” design. Commonly used experimental techniques including Taguchi methods require many unneeded runs when applied to numerical methods. They also make insupportable assumptions about interactions being zero, not allowing the user to fit commonly used non-linear models. We describe how our method with 36 runs is likely to give better results than Taguchi methods using 162 runs.