Rethinking Steepest Ascent
The path of steepest ascent proposed by Box and Wilson (1951) consists of points that maximize the predicted response for a fitted first-order model among all points with the same standard error of prediction. This method is frequently used by practitioners. However, when there are multiple responses or additional constraints (e.g., on cost or throughput), standard steepest ascent is of limited usefulness, since it often optimizes one response at the expense of others. The question of interest is whether there exist compromise directions that ensure improvement in all responses. We address the problem by constructing confidence bounds for improvement of each response relative to its performance at the center of the design. Overlaying these confidence regions provides the user with the best insight regarding the benefit of different search directions. Additionally, we propose a plot showing the efficient improvement frontier for pairs of response variables. While literature often deals with multiple response optimization in the later stages of response surface exploration, our article addresses how to proceed following a successful initial screening experiment.
desirability function efficient frontier optimization response surface methodology.
Robert Mee Jihua Xiao
Department of Statistics, Operations, and Management Science University of Tennessee Knoxville, TN 37996-0532
国际会议
2006 International Conference on Design of Experiments and Its Applications(2006实验设计及其应用国际会议)
天津
英文
2006-07-09（万方平台首次上网日期，不代表论文的发表时间）