Model robust response surface designs: Scaling two-level factorials

Response surface methods use simple graduating functions to study the relationship between an experimental response variable and a set of continuous explanatory variables. In designing a response surface study, an experimenter must decide how far apart to set the levels of each factor, i.e. how to scale the design. A good choice should be sensitive to the fact that the graduating function is only an approximation to the true response function. A Bayesian model is proposed that makes explicit assumptions about inadequacy of an assumed model and a design criterion based on the model leads to reasonable choices of scale for two-level factorial designs. The choice of scale is found to insensitive to the prior distributions in the model.