Title: Predictive models for functional responses in mixture experiments using SVEM: a case study in rheological analysis

Authors: Mona Khoddam; Michelle V. Mancenido; Hossein Tohidi; Douglas C. Montgomery

Addresses: School of Computing and Augmented Intelligence, Arizona State University, Tempe, Arizona, USA ' 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 extensively used in applications where the experimental factors are varying proportions of components or ingredients that sum to a constant. While much research on mixture experiments has focused on singular response values, numerous chemical or formulation experiments form a sequence of data points over a continuum, i.e., functional data. Earlier studies introduced techniques for functional data analysis (FDA) within factorial experiments, but analysing it in mixture experiments poses challenges due to the intricate functional response surface and inherent linear interdependence within the factor subspace. This study examines a real-world case study where a mixture experiment's outcome yield functional data. Relying on a single viscosity value at a set shear rate overlooks diverse rheological distinctions among chemical formulations. Various FDA models are investigated for their fit, predictive capability, and ease of interpretation, in self-validating ensemble models (SVEM). Finally, mixture formulation is optimised to meet customer and business objectives.

Keywords: mixture experiments; functional data analysis; FDA; self-validating ensemble models; SVEM; D-optimal designs; experimental design.

DOI: 10.1504/IJEDPO.2024.140476

International Journal of Experimental Design and Process Optimisation, 2024 Vol.7 No.2, pp.135 - 152

Received: 01 Oct 2023
Accepted: 23 Jan 2024
Published online: 19 Aug 2024 *

Full-text access for editors Full-text access for subscribers Purchase this article Comment on this article