Abstract 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. Keywords: Sequential empirical optimizationresponse surface methodsdual controlcost to godynamic programming Acknowledgement We thank two anonymous referees whose comments help improve our presentation.