Design augmentation for response optimization and model estimation

ABSTRACT

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.

KEYWORDS:

• definitive screening design
• optimal design
• response surface
• ridge trace
• sequential experimentation
• steepest ascent

About the authors

Christopher J. Nachtsheim is a professor and the Frank A. Donaldson Chair of Operations Management in the Supply Chain and Operations Department in the Carlson School of Management at the University of Minnesota. Dr. Nachtsheim's teaching and research interests center on the optimal design of industrial experiments, regression and predictive modeling, and quality management. He is a four-time recipient (1991, 2009, 2011, and 2015) of the Brumbaugh Award of the ASQ for best paper published in the area of industrial quality control, two-time recipient of the Lloyd S. Nelson Award of the ASQ for the published paper having the greatest impact on practitioners (2010 and 2012).

Bradley Jones is Principal Research Fellow in the JMP division of SAS. He developed the Custom Designer, a general and powerful tool for generating optimal experimental designs and invented the prediction profile plot - an interactive graph for exploring multivariate response surfaces. He is co-discoverer with Chris Nachtsheim of Definitive Screening Designs. He has won the Youden Prize, and both the Brumbaugh and the Lloyd S. Nelson awards twice from the American Society for Quality. He is a past editor of the Journal of Quality Technology.