Three-Level Simplex Designs and Their Use in Sequential Experimentation

This article first presents three-level simplex designs of k+1 runs for k factors. 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 inclusion of a block effect in the fitted second-order model. Revised February 21, 2001 Dr. Mee is Professor and Head of the Department of Statistics. He is a member of ASQ.