D-Optimal Design

D-Optimal Design is the most widely used optimal experimental design criterion — selecting the set of experimental runs that maximizes the determinant of the information matrix ($X^TX$), resulting in the smallest possible confidence region for the estimated model parameters.

How D-Optimal Design Works

• Candidate Set: Generate a large set of candidate design points within the factor space.
• Algorithm: Exchange algorithms (Fedorov, coordinate exchange) iteratively swap candidate points to maximize $|X^TX|$.
• Model: Specify the regression model (linear, quadratic, interaction terms) that will be fit.
• Output: The selected subset of candidate points forms the D-optimal design.

Why It Matters

• Most Precise Estimates: D-optimal designs provide the most statistically precise parameter estimates.
• Flexible: Works with any number of factors, levels, and model terms — no preset templates needed.
• Constraints: Handles factor constraints, mixture constraints, and irregular design regions naturally.

D-Optimal Design is the most informative experiment — choosing experimental runs to maximize the precision of the estimated model coefficients.