Quantile Plots of the Prediction Variance for Partially Replicated Central Composite Design

Abstract

Sometimes, it is not feasible to fully replicate the experimental units. When this happen, there is need for optimal replication of the experimental units to avoid bias. The prediction variance of two variations of the partially replicated central composite design (replicated cube plus one star and one cube plus replicated star) are compared using the quantile plots. These plots provide information about the prediction variance distribution on a sphere for comprehensive evaluation of the quality of the prediction variance. For face-centred (α = 1) and rotatable (α = F 1 4 ) central composite designs, the prediction variance of the one cube plus replicated star perform better than the replicated cube plus one star. Unlike the replicated cube plus one star, the quantile plots of the scaled prediction variance of the one cube plus replicated star depict near rotatability.

Optimal Prediction Variance Capabilities of Inscribed Central Composite Designs

“…They concluded that the replicated-star options always give smaller G-and I-optimal values than the corresponding replicated-cube options with equal number of replications. In [9] the author(s) used quantile plots to compare the prediction variance of partially replicated face center cube and rotatable central composite design. They concluded that the performance of the factorial with replicated axial points in both design is preferred to the replicated factorial portion with one axial portion.…”