A Prediction Region-based Approach to Model Uncertainty for Multi-response Optimization

Abstract

Multi-response optimization methods rely on empirical process models based on the estimates of model parameters that relate response variables to a set of design variables. However, in determining the optimal conditions for the design variables, model uncertainty is typically neglected, resulting in an unstable optimal solution. This paper proposes a new optimization strategy that takes model uncertainty into account via the prediction region for multiple responses. To avoid obtaining an overly conservative design, the location and dispersion performances are constructed based on the best-case strategy and the worst-case strategy of expected loss. We reveal that the traditional loss function and the minimax/maximin strategy are both special cases of the proposed approach. An example is illustrated to present the procedure and the effectiveness of the proposed loss function. The results show that the proposed approach can give reasonable results when both the location and dispersion performances are important issues. Copyright (c) 2015 John Wiley & Sons, Ltd.