An adaptive Bayesian approach for robust parameter design with observable time series noise factors

In Robust Parameter Design (RPD) the means and the covariances of noise variables, commonly assumed as known, are estimated from operating or historical data and hence can involve considerable sampling variability. In addition, for cases where there are noise factors that are measurable or with strong autocorrelation a more effective control strategy is to update the estimates of noise factor as the production takes place. This article presents a Bayesian approach to online RPD that accounts for uncertainty in noise factor and response models and allows the user to update the model estimates with production data and achieve more effective control performance. The proposed method is compared to existing dual response and certainty equivalence control approaches from the literature. Simulation examples and a case study that uses real manufacturing data from an injection molding process are used to demonstrate the proposed method.