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

Summary: [This abstract is based on the authors' 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.

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  • Topics: Design of Experiments, Process Management
  • Keywords: Case study, Computer-Aided Design (CAD), Mixture experiments, Split-plot design, Design of experiments (DOE), D-efficiency, Optimal design, Process optimization, Pareto charts, Randomization tests
  • Author: Lu, Lu; Robinson, Timothy J.; Anderson-Cook, Christine M.;
  • Journal: Quality Engineering