Using genetic algorithms to generate mixture-process experimental designs involving control and noise variables

Genetic algorithms are useful techniques for generating statistical designs when standard factorial and response surface methods either cannot be easily applied or they perform poorly. These situations often occur when the design space is highly constrained and irregular, we are using nonstandard models, or the criteria for design evaluation are complicated. We consider statistical designs for experiments involving mixture variables and process variables, some of which are noise variables that cannot be controlled under general operating conditions. For these types of experiments, it is customary to fit a response model combining mixture, process, and noise variables and to derive a model for the mean response and a model for the slope of the response. When considering experimental designs to use for these situations, low prediction variances for the mean and slope models are desirable. We evaluate some standard mixture-process variable designs with respect to these criteria and demonstrate how an experimenter can create designs with improved scaled prediction variance (SPV) properties using a genetic algorithm.