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Unlike standard classical designs such as factorials and fractionalfactorials, D-optimal design matrices are usually not orthogonal andeffect estimates are correlated.
These types of designs are always an option regardless of the type ofmodel the experimenter wishes to fit (for example, first order,first order plus some interactions, full quadratic, cubic, etc.) orthe objective specified for the experiment (for example, screening,response surface, etc.). Desktoppr 1 826. D-optimal designs are straight optimizationsbased on a chosen optimality criterion and the model that will be fit.The optimality criterion used in generating D-optimal designs is one ofmaximizing X'X , the determinant of the information matrix X'X.
This optimality criterion results in minimizing the generalized varianceof the parameter estimates for a pre-specified model. As a result, the'optimality' of a given D-optimal design is model dependent. That is,the experimenter must specify a model for the design before a computercan generate the specific treatment combinations. Given the totalnumber of treatment runs for an experiment and a specified model, thecomputer algorithm chooses the optimal set of design runs from acandidate set of possible design treatment runs. This candidateset of treatment runs usually consists of all possible combinations ofvarious factor levels that one wishes to use in the experiment.
In other words, the candidate set is a collection of treatmentcombinations from which the D-optimal algorithm chooses the treatmentcombinations to include in the design. The computer algorithm generallyuses a stepping and exchanging process to select the set of treatmentruns.
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Note: There is no guarantee that the design the computergenerates is actually D-optimal.