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Publication date: 07/24/2024

Design Efficiency

In the Evaluate Design platform, D, G, and A, efficiency is reported. The descriptions of the efficiency measures use the following notation:

X is the model matrix

n is the number of runs in the design

p is the number of terms, including the intercept, in the model

Equation shown here is the relative prediction variance at the point Equation shown here. See “Relative Prediction Variance”.

Equation shown hereis the maximum relative prediction variance over the design region

D Efficiency

The efficiency of the design to that of an ideal orthogonal design in terms of the D-optimality criterion. A design is D-optimal if it minimizes the volume of the joint confidence region for the vector of regression coefficients:

Equation shown here

G Efficiency

The efficiency of the design to that of an ideal orthogonal design in terms of the G-optimality criterion. A design is G-optimal if it minimizes the maximum prediction variance over the design region:

Equation shown here

Letting D denote the design region,

Equation shown here

Note: G-Efficiency is calculated using Monte Carlo sampling of the design space. Therefore, calculations for the same design might vary slightly.

A Efficiency

The efficiency of the design to that of an ideal orthogonal design in terms of the A-optimality criterion. A design is A-optimal if it minimizes the sum of the variances of the regression coefficients:

Equation shown here

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