Experimental designs for constrained regions

The familiar factorial, fractional factorial, and response surface designs are designs for regularly-shaped regions of interest, typically cuboidal regions and spherical regions. An irregularly shaped region of experimentation arises in situations where there are constraints on the factor level combinations that can be run or restrictions on portions of the region of exploration. Computer-generated designs based on some optimality criterion are a logical alternative for these problems. We give a brief tutorial on design optimality criteria and show how one of these, the D-optimality criteria, can lead to very reasonable designs for constrained regions of interest. We show through a simulation study that D-optimal designs perform very well with respect to the capability of selecting the correct model and accurately estimating the design factor levels that result in the optimal response.