Optimal designs with axial values

We introduce a modification to the coordinate-exchange algorithm for generating optimal experimental designs that incorporates off-face axial value runs similar to a central composite design (CCD). This improvement addresses a weakness of current optimal designs relative to classical designs: the superior properties of CCDs with off-face axial values relative to equal-sized optimal designs that are constrained to the cuboidal experimental design region. CCDs tend to have significantly less collinearity among quadratic effects, which results in higher power for quadratic terms, better D-efficiency, and lower average prediction variance (i.e., I-optimality). Optimal designs offer greater flexibility in design size, model specification, and the ability to incorporate categorical factors. By incorporating axial values into an optimal design algorithm, the strengths of both approaches can be combined in a single design that generally outperforms both CCDs and current optimal designs.