Factorwise variance dispersion graphs

Abstract

In this paper, new plots, called factorwise variance dispersion graphs (FVDGs) with accompanying coordinate trace plots (CTPs), are introduced. FVDGs display prediction variances throughout the design space across the levels of each design factor, while CTPs plot the coordinates associated with minimum and maximum prediction variances, and hence G-efficiencies. FVDGs and CTPs can supplement the use of other graphical tools (e.g., variance dispersion graphs and fraction of design space plots) when assessing the prediction variance properties of a response surface design. They also can be used to assess the robustness of designs with respect to model reduction, design augmentation, and with an irregular design space as in a mixture experiment. Examples and the benefits of FVDGs and CTPs will be presented.

Keywords:

• Componentwise variance dispersion graphs
• Fraction of design space plots
• G-efficiency
• Prediction variance
• Variance dispersion graphs