A Case Study to Select an Optimal Split-Plot Design for a Mixture-Process Experiment Based on Multiple Objectives

ABSTRACT

With increasingly constrained budgets, it is now becoming more desirable to get more information from each experiment and to have an intentional strategy for selecting designs for split-plot experiments that balance multiple competing objectives. Lu and Anderson-Cook (2014) developed a decision-making process for selecting an optimal split-plot design (SPD) for flexible objectives/criteria based on a Pareto front. The method allows exploration of all contending non-inferior choices with their trade-offs to enable an informed and justifiable decision based on understanding the potential impact of subjective aspects. This article considers a case study of a mixture-process experiment that seeks an SPD with a good balance of precise model coefficient estimates as measured by D-efficiency and low experimental cost, which is a function of both the time required to run the experiment as well as the financial cost. The D-efficiency is a function of the whole plot-to-subplot error variance ratio, a quantity that is typically not known a priori when the choice of a design must be made. The Pareto front approach is applied and graphical tools are used to quantify the trade-offs between criteria and robustness of design performance to different user-selected preferences for the criteria. A substantially different pattern of design performance robustness to the uncertainty of the specified variance ratio is demonstrated compared to non-mixture experiments.

KEYWORDS:

• computer-generated designs
• restricted randomization
• multiple design criteria
• design optimization
• D-optimality
• cost
• Pareto front
• point exchange search algorithm

Additional information

Notes on contributors

Lu Lu

Dr. Lu Lu is a visiting assistant professor at the University of South Florida and was a postdoctoral research associate with the Statistical Sciences Group at Los Alamos National Laboratory. Her statistical research interests include reliability, design and analysis of experiments, response surface methodology, survey sampling, and analysis. She is a graduate of the Statistics Department at Iowa State University.

Timothy J. Robinson

Dr. Timothy J. Robinson is the Director of the WWAMI Medical Education Program and a Professor in the Department of Statistics. He is a Fellow of the American Statistical Association and a Fellow of ASQ. His e-mail address is [email protected].

Christine M. Anderson-Cook

Dr. Christine M. Anderson-Cook is a research scientist in the Statistical Sciences Group at Los Alamos National Laboratory. Her research interests include design of experiments, reliability, and response surface methodology. She is a Fellow of the American Statistical Association and the American Society for Quality.