Sequential “asymmetric” D-optimal designs: a practical solution in case of limited resources and not equally expensive experiments

When the cost of an experiment depends on the values of the variables not all the experiments are equally expensive. Since in all the standard Designs of Experiments the experiments are symmetrically distributed, in case of finite resources the number of experiments is limited by the cost of the most expensive ones. The approach here shown produces asymmetrical designs, with an increase of the number of the cheapest experiments and a decrease of the number of the expensive ones. Compared to the standard designs having the same total cost, the information obtained by this strategy is slightly worse in the region corresponding to the most expensive experiments, but much better in the region corresponding to the cheapest experiments. This approach was successfully applied to the micronization of an Active Pharmaceutical Ingredient.