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In a complex system, large numbers of design variables and responses are involved in performance analysis. Relationships between design variables and individual responses can be complex, and the outcomes are often competing. In addition, noise from manufacturing processes, environment, and customer misusage causes variation in performance. The proposed method utilizes the two-step optimization process from robust design and performs the optimization on multiple responses using Hotelling's T2 statistic. The application of the T2-statistic allows the use of univariate tools in multiple objective problems. Furthermore, the decomposition of T20 into a location component, T2M and a dispersion component, T2D substitutes a complex multivariate optimization process with the simpler two-step procedure. Finally, using information from the experiment, a multivariate process capability estimates for the design can be made prior to hardware fabrication.