Variance Dispersion Graphs (VDGs) are useful summaries for comparing competing designs on a fixed design space. However, they do not give all useful information about the prediction capability of a design. We propose the Fraction of Design Space (FDS) technique, which addresses some of the shortcomings of VDGs. The new technique gives the researcher more detailed information by quantifying the fraction of design space where the scaled prediction variance (SPV) is less than or equal to any pre-specified value. The FDS graph gives the researcher information about the distribution of the SPV in the region based on the ranges and proportions of possible SPV values. Several variations on the graph, including plotting the variance of the estimated mean response, are also presented to allow for specialized consideration of different designs. The FDS technique complements the use of VDGs to give the researcher more insight into the prediction capability of a design. Several standard designs with different numbers of factors are studied with both methods.

Variance dispersion graphs are useful tools for evaluating various types of designs, including mixture and mixture-process designs. They allow an experimenter to see patterns of scaled prediction variances (SPV) throughout a design space. We introduce a complementary fraction of design space (FDS) plot that provides additional information on the distribution of the SPV throughout a design space. These plots display the fraction of design space where the SPV is less than or equal to specific values. The FDS plots for combined mixture-process experiments also show which of the two types of variables has more influence on the SPV. The FDS plots for mixture and mixture-process experiments are developed and then demonstrated with several examples.

When choosing between competing designs, it is typical to specify a design space and model on which to base the comparison. The prediction capabilities of the design, specifically G- and V-efficiency using scaled prediction variance (SPV), are based on this chosen model. After the data are collected and individual effects are tested, some terms may not be significant in the model. In this case, the experimenter likely will decide to use a reduced model, which has only a portion of the terms included that were in the original model for which the design was chosen. This paper presents a graphical method for examining design robustness related to the SPV values using fraction of design space (FDS) plots by comparing designs across a number of potential models in a prespecified model space. The FDS plots show the various distributions of the SPV throughout the design space for different models for a chosen design on the same graph. The methods are demonstrated on several examples for different models and on a variety of design spaces.