The incorporation of robustness criteria in process design under uncertainty is a key issue to derive optimal designs for quality. This article presents a systematic design framework for process quality that embeds Taguchi's method within a stochastic optimization formulation. The problem is formulated as a single-level optimization problem with expected objective function values computed by an efficient cubature technique. The solution obtained determines an optimal design together with a robust operating policy that maximize average process performance. A process example of a reactor and heat exchanger is provided.