A new approach to the sequential design of experiments for the rapid optimization of multiple response, multiple controllable factor processes is presented. The approach is Bayesian and is based on an approximation of the cost to go of the underlying dynamic programming formulation. The approximation is based on a matrix T posterior predictive density for the predicted responses over the length of the experimental horizon that allows the responses to be cross-correlated and/or correlated over time. The case of an unknown variance is addressed; the assumed models are linear in the parameters but can be nonlinear in the factors. It is shown that the proposed approach has dual-control features, initially probing the process to reduce the parameter uncertainties and eventually converging to the desired solution. The convergence of the proposed method is numerically studied and convergence conditions discussed. Performance comparisons are given with respect to a known-parameters controller, the efficient global optimization algorithm, popular in sequential optimization of deterministic engineering metamodels, and with respect to the classical use of response surface designs followed by an optimization step.
Two common experimental designs used in robust parameter design (RPD) are crossed array and mixed resolution designs. However, the prohibited number of runs, constraints in the design space or special model requirements render some of these designs inadequate. This paper presents the application of an evolutionary strategy to produce nearly optimal design matrices for RPD. The designs are derived by solving a nonlinear optimization problem involving both D-and G-efficiency simultaneously. The methodology presented allows the user to obtain new exact designs for a specific number of runs, and a particular experimental region. The combination of D-and G-efficiency results in experimental designs that outperform the corresponding benchmarks.
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