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Replication of the factorial (cube) and/or axial (star) portions of the central composite design (CCD in response surface exploration has gained great attention recently. Some well known metrics (called single-value functions or criteria) and graphical methods are utilized in evaluating the regression based response surface design. The single-value functions considered here are the A-efficiency, and the D-efficiency, , where , k is number of factors,  is the kth design measure, is the design’s information matrix,  is its inverse and N is the total number of experimental runs. These two functions are very popular in parameter estimation in response surface methodology. The exact measures of these two design criteria will be developed analytically in this work to account for partial replication of the cube and/or star components of the CCD. This will alleviate the burden of manual computation of these metrics when there are partial replications and reduce over reliance on software values which, often, are approximate values and maybe inaccurate.

Modified Exact Single-Value Criteria for Partial Replications of the Central Composite Design