Quantile Dispersion Graphs for Assessing the Prediction Capability of Third-Order Box-Behnken Designs

Abstract

The prediction capability of response surface models within a specified experimental region depends on the magnitude and behaviour of the scaled prediction variance (SPV). In this paper, quantile dispersion graphs (QDGs), boxplots and a prediction performance measure were used to assess the distribution, stability, and prediction capability of three third-order Box-Behnken designs: augmented Box-Behnken designs (ABBDs), augmented fractional Box-Behnken designs (AFBBDs), and new augmented Box-Behnken designs (NABBDs). The assessment was conducted for 3 ≤ k ≤ 6 factors using 1 ≤ nc ≤ 3 centre points. The results show that AFBBDs consistently provide superior predictive capability, particularly at moderate and large radii, while ABBDs demonstrate greater stability near the design centre. NABBDs perform least well across most radii. Overall, AFBBDs are identified as the most efficient of the three designs for providing accurate third-order response surface predictions across the experimental region.