Shrinkage simplex-centroid designs for a quadratic mixture model

Authors

1 Department of Industrial Engineering, Yazd University, Pajoohesh Square, Yazd, 89195741, Iran

2 School of Industrial and Systems Engineering, University of Tehran, Tehran, Iran

3 Department of Statistics, Islamabad Model College for Boys, Sector F-10/4, Islamabad, Pakistan

4 School of Business and Economics, Lahore, Pakistan

5 Department of Mathematics, Islamabad Model College for Boys, Sector F-10/4, Islamabad, Pakistan

Abstract

A simplex-centroid design for q mixture components
comprises of all possible subsets of the q components,
present in equal proportions. The design does not
contain full mixture blends except the overall centroid. In
real-life situations, all mixture blends comprise of at least a
minimum proportion of each component. Here, we introduce
simplex-centroid designs which contain complete
blends but with some loss in D-efficiency and stability in
G-efficiency. We call such designs as shrinkage simplexcentroid
designs. Furthermore, we use the proposed designs
to generate component-amount designs by their projection.

Keywords