In stochastic process design and planning optimization problems, the expected value of the objective function in face of uncertainty is typically evaluated through an n-dimensional integral, where n is the number of uncertain parameters. In this paper, suitable integration techniques are presented and computational issues are discussed in relation to the number of uncertain parameters and the uncertainty model considered. A specialized cubature technique, suitable to integrate normally distributed uncertainties, is introduced, which for n < 10 can reduce significantly the computational effort required when compared to other strategies, such as product Gauss rules or efficient sampling techniques. The computational performance of the different integration techniques and their applicability are discussed through two process-engineering examples.

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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.

The fundamental principles of chemical product design and associated systematic tools, within a broad domain of chemical products including molecules, formulations, and devices, are still under development. In this article, we propose a simple and fundamental conceptual model that defines the chemical product design problem as the inversion of three central design functions: quality, property, and process functions. The classic iterative cycles of product design problems may be envisioned as alternating between inversion and evaluation of these three functions, or in other words alternating between synthesis and analysis of solutions. On top of the proposed basic structure of the overall design problem, we then discuss the formulation of some subproblems as optimization problems and describe some useful solution tools. Three application examples are provided, including a more detailed case of formulation of a pharmaceutical ointment. © 2014 American Institute of Chemical Engineers AIChE J, 61: 802–815, 2015