A Bayesian model-averaging approach for multiple-response optimization

Abstract

The characteristics that define the quality and reliability of many products and processes are often multidimensional. Many of the current multiple-response optimization approaches assume a single-response model to optimize such processes and do not consider the correlations among the response data, the uncertainty in the response models, and the uncertainty in the parameter estimates of the models. Failure to account for these uncertainties can result in misleading quality estimates and therefore poor process design. In this paper, we consider a Bayesian decision theoretic approach to the modeling and optimization of multiple-response systems. This approach naturally accounts for the correlations among the responses, the variability of the predictions, and the uncertainty of the model parameters. We further propose a Bayesian model averaging approach to account for response-model uncertainty. This approach is general and enables the consideration of many types of quality criteria and characteristics. In addition, we also consider the important follow-up question of how to allocate further resources for additional experimentation to achieve or improve on the desired quality level.