Title: Constructing D-optimal designs for mixture-process variable experiments with binary responses

Authors: Mona Khoddam; Hossein Tohidi; Douglas C. Montgomery

Addresses: School of Computing and Augmented Intelligence, Arizona State University, Tempe, Arizona, USA ' SAS Institute Inc., Cary, NC, USA ' School of Computing and Augmented Intelligence, Arizona State University, Tempe, Arizona, USA

Abstract: Mixture experiments are widely applied in various fields to analyse responses influenced by component proportions that sum to a constant. While classical mixture experiments focus solely on these proportions, mixture-process variable (MPV) experiments also incorporate additional non-mixture factors. Introducing process variables into the model significantly increases the complexity of the experimental design. Additionally, binary responses pose further challenges, as traditional designs for continuous responses under normal-theory linear models often fail to perform adequately in such scenarios. This research proposes an exchange algorithm to generate D-optimal designs for MPV experiments with binary responses. The algorithm effectively addresses key challenges, including the nonlinear nature of the D-optimality criterion, the interaction between mixture and process variables, and the need for prior parameter estimates. The method demonstrates robustness and efficiency by producing stable designs across varying sizes while achieving high D-optimality scores. By bridging the gap in experimental design for binary responses, this work enhances the applicability of MPV experiments in industrial and scientific research. The findings highlight the importance of tailored approaches for binary responses and lay the foundation for future advancements in experimental design methodologies spanning diverse applications.

Keywords: mixture-process variable experiments; binary responses; logistic regression; D-optimality; coordinate exchange algorithm.

DOI: 10.1504/IJEDPO.2025.152110

International Journal of Experimental Design and Process Optimisation, 2025 Vol.8 No.1/2, pp.15 - 35

Received: 10 Jan 2025
Accepted: 08 Mar 2025
Published online: 09 Mar 2026 *

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