On The Optimal Choice of Cube and Star Replications in Restricted Second-Order Designs

Abstract

This article examines the central composite design in which some of the experimental runs are replicated. Three different classes of N-point designs are compared using the criterion of Schur's ordering under orthogonality, rotatablity, and slope- rotatablity conditions. The response surface designs with the star portion replicated seem to have more potential than others under orthogonality condition, while the designs with the cube portion replicated is preferable to the designs with their star portion or only the center point replicated under rotatable and slope-rotatable conditions.

Keywords::

• Central composite designs
• Orthogonal designs
• Rotatable designs
• Slope-rotatable designs
• Schur's ordering of designs

Mathematics Subject Classification:

• Primary 62K05
• Secondary 62K20