Robust parameter design (RPD) is implemented in systems in which a user wants to minimize the variance of a system response caused by uncontrollable factors while obtaining a consistent and reliable system response over time. We propose the use of artificial neural networks to compensate for highly non-linear problems that quadratic regression fails to accurately model. RPD is conducted under the assumption that the relationship between system response and controllable and uncontrollable variables does not change over time. We propose a methodology to find a new set of settings that will be robust to moderate system degradation while remaining robust to noise variables within the system RPD has been well developed on single response problems. Sparse literature exists on dealing with multiple responses in RPD and most methods utilize a subjective weighting scheme. To account for multiple responses, we examine the use of factor analysis on the response data. All the proposed techniques are applied to textbook applications to demonstrate their utility. An Air Force application problem is examined to demonstrate the new technique's potential on a real-world problem that is highly non-linear. The application is a detector developed to detect anomalies within hyper-spectral imagery.