What are “optimal designs” and “optimality criteria”?

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JMP’s Custom Design platform allows experimenters to create custom-built designs for their specific experiment needs by constructing optimal designs. The custom designer generates optimal designs by seeking to maximize one of several optimality criteria using the coordinate-exchange algorithm. The coordinate-exchange algorithm constructs a starting design by selecting random values within the design region specified for each factor and run. The found design is only locally optimal and the coordinate-exchange algorithm is repeated many times to improve the probability of finding a globally optimal design. Custom Design provides the design that maximizes the optimality criterion among all the constructed designs.

The optimality criteria include:

• D-optimality
• I-optimality
• A-optimality
• Alias-optimality

Optimality criteria can be specified under the red triangle in Custom Design.

The recommended (default) optimality criteria are:

Model specified in Custom Design	Default optimality criterion
Full quadratic model using the RSM button	I-optimality
Models with two-factor interactions added via interactions button	A-optimality
In all other cases	D-optimality

The goal of the design is behind the reasoning for both the default optimality criteria used and when one would change from the default optimality criterion to other optimality criteria such as alias-optimal.

From a high-level point of view, there are two goals for running experimental designs: identifying active effects (screening) and optimizing a response (prediction). First-order models (main effect models) are used for identifying active effects in screening designs. D-optimal focuses on minimizing the error of coefficients so it lends itself to identifying active effects.

Second-order models (main effects plus quadratics and two-way interactions) are used when optimizing operating settings for your process and the prediction of the response takes priority over exact parameter estimation. I-optimal addresses prediction variance and so is the recommended (default) optimality criteria for second-order models using the RSM button when defining the model in Custom Design.

Optimality criterion	Goal of experimental design	Practical goal
I-optimal	Minimizing prediction variance	Accurate predictions
D-optimal	Minimizing error of coefficients	Understand factor relationships
A-optimal	Weighting different parts of the model	Understand factor relationships focusing on specific factors of interest
Alias-optimality	Eliminating correlations of main effect (ME) with two-factor interaction (2FI).	Understand factor relationships where MEs are unbiased by possible large active 2-FIs

Example of how to specify and identify the optimality criteria in Custom Design: