The construction of robust mixture-process experimental designs via genetic algorithm

Mixture experiments with the presence of process variables are commonly encountered in the manufacturing industry. The experimenter who plans to conduct mixture experiments in which a process involves the combination of machines, methods, and other resources will try to find condition of design factors which make the product/process insensitive or robust to the variability transmitted into the response variable. We propose the genetic algorithm (GA) for generating robust mixture-process experimental designs involving control and noise variables. When the noise variables, which are extremely difficult to control or not routinely controlled during the manufacturing process and may change without warning, are considered in a mixture experiment, we propose the robust design setting. When considering a robust design, the design that has a lower and flatter faction of design space curves for all levels of the controllable process variables at varying noise interaction is preferable. We evaluate the designs with respect to these criteria for both the mean model and the slope model. The evaluation demonstrates that the proposed GA designs are robust to the contribution of the interactions involving the noise variables.