Three-Level Simplex Designs and Their Use in Sequential Experimentation

Abstract

In this paper three-level simplex designs of k+1 runs for k factors are presented. Each simplex design is composed of k treatment combinations from a two-level factorial design, plus an additional base run that represents a third level for each factor. These orthogonal, first-order designs are simple to construct. Furthermore, simplex designs can be augmented to construct second-order simplex sum designs. Such designs are particularly attractive when the experimental region of interest is spherical rather than a hypercube. It is also noted that the k treatment combinations in each simplex design coincide with the axial points in the second-order, asymmetric composite designs proposed by Box and Wilson (1951) and later discussed by Lucas (1974). Including the base point permits the inclusion of a block effect in the fitted second-order model.