Steepest ascent improvement by response predictions implementation

Abstract

For the exploratory runs of steepest ascent the use of response predictions is proposed. The factors for these runs are estimated on the data of initial experiment and by finding conditional extremum. Parameter estimates are employed to obtain estimated response functions on which the response of exploratory runs is predicted. Response prediction intervals for these runs are found by using the parameter estimates of linear models, factor estimates for exploratory runs, and linear models for response predictions. This allows to identify those response observations that go beyond the bounds of response prediction intervals and to find factor values under which exploratory run response at hand is still in its prediction interval. The comparison of two linear models reveals that the model with coded factors and response variables allows to obtain the smaller intervals of response predictions. This permits to identify more accurately the last run of steepest ascent and factor levels for design centre of the next initial experiment.