Confidence Regions for Constrained Optima in Response-Surface Experiments

The precision of the estimated optimum from a response-surface experiment is often indicated via a confidence region about the optimum. Sometimes, because of associated secondary responses, unconstrained optima produce unrealistic operating conditions, even when the true response surface is known. We consider confidence intervals for constrained optima for which the constraint function is known or separately estimated. An example from a cancer combination chemotherapy experiment illustrates the construction of such a region.