Design augmentation for response optimization and model estimation

In this article, we consider a situation in which an investigator has run an initial screening experiment, has eliminated some inactive factors, and has undertaken a second stage of experimentation in an effort to identify the optimal operating conditions. If sequential experimentation is possible, the standard approach to this problem is to identify the direction of steepest ascent (descent), and to conduct a series of runs in that direction. Once the best operating conditions in that direction are identified, further experimentation in the new neighborhood can be conducted. Unfortunately, this direction may be poorly estimated or irrelevant depending on the magnitude of experimental error and the nature of the underlying response model. We advocate here the use of optimally augmented experiments in the general direction of a ridge trace. We evaluate alternative strategies using simulation and compare the best of these strategies to method of steepest ascent.