Quantile Plot Visualization of Central Composite Designs in Multidimensional Space

Abstract

This study assesses and compares the prediction variances (PV) of competing response surface designs, including Central Composite Design (CCD), Small Composite Design (SCD), and Minimum Run Resolution (MinRes) V designs. While traditional single-value optimality criteria (A-, D-, G-, and I-optimality) and prediction-based assessments such as Variance Dispersion Graphs (VDG) and Fraction of Design Space (FDS) provide useful insights, they fall short of fully characterizing the distribution of PV across the design space. Consequently, quantile plots are employed to examine the stability and prediction capability of these designs, providing a more comprehensive assessment of their performance. The results reveal clear differences in the distribution and stability of prediction variances among the designs, with some designs exhibiting more robust and uniform predictive behaviour across the experimental region. These findings demonstrate that quantile plots offer valuable complementary information beyond conventional criteria and support more informed design selection in response surface methodology, thereby improving prediction reliability and experimental efficiency.