Model-robust process optimization using Bayesian model averaging

Traditional approaches for process optimization start by fitting a model and then optimizing the model to obtain optimal operating settings. These methods do not account for any uncertainty in the parameters of the model or in the form of the model. Bayesian approaches have been proposed recently to account for the uncertainty on the parameters of the model, assuming that the model form is known. This article presents a Bayesian predictive approach to process optimization that accounts for the uncertainty in the model form, also accounting for the uncertainty of the parameters given each potential model. We propose optimizing the model-averaged posterior predictive density of the response where the weighted average is taken using the model posterior probabilities as weights. The resulting model-robust optimization is illustrated with two experiments from the literature, one involving a mixture experiment and the other involving a small composite design.