Bayesian approaches for on-line robust parameter design

Two new Bayesian approaches to Robust Parameter Design (RPD) are presented that recompute the optimal control factor settings based on on-line measurements of the noise factors. A dual response model approach to RPD is taken. The first method uses the posterior predictive density of the responses to determine the optimal control factor settings. A second method uses in addition the predictive density of the noise factors. The control factor settings obtained are thus robust not only against on-line variability of the noise factors but also against the uncertainty in the response model parameters. On-line controllable and off-line controllable factors are treated in a unified manner through a quadratic cost function. Both single and multiple-response processes are considered and closed-form robust control laws are provided. Two simulation examples and an example taken from the literature are used to compare the proposed methods with existing RPD approaches that are based on similar models and cost functions.