The identification and incorporation of quality costs and robustness criteria is becoming a critical issue while addressing chemical process design problems under uncertainty. This article presents a systematic design framework that includes Taguchi loss functions and other robustness criteria within a single-level stochastic optimization formulation, with expected values in the presence of uncertainty being estimated by an efficient cubature technique. The solution obtained defines an optimal design, together with a robust operating policy that maximizes average process performance. Two process engineering examples (synthesis and design of a separation system and design of a reactor and heat exchanger plant) illustrate the potential of the proposed design framework. Different quality cost models and robustness criteria are considered, and their influence in the nature and location of best designs systematically studied. This analysis reinforces the need for carefully considering/addressing process quality and robustness related criteria while performing chemical process plant design.