D-Optimal Design with Split Plot Approach for Quadratic Mixture-Amount Experiments (Case Study of Three Components with Composition Constraints)

Abstract

The mixture experiments (MAE) were influenced by both the proportions of the components and the total amount. The traditional MAE encompasses classical mixture experiments for each total amount, which complicates the application of complete randomization; therefore, a split-plot design is suggested. In this design, the plot factor represents the total mixture amount, whereas the subplot represents the composition of the materials. Another issue is the increasing number of experiments as the number of materials and total amount increase. This study proposes a split-plot approach using a point-exchange algorithm based on the D-optimal criteria to generate an efficient design. The model used is a quadratic mixture of numbers model, which can capture the linear, quadratic, and interaction effects between material proportions and total mixture numbers. The case study involved three components with proportion constraints and three levels of mixture numbers: high, medium, and low. The results show that the algorithm generates optimal points generally located at the edge of the design region and that increasing the number of experimental units improves the stability of designs involving total mixture numbers.