Evaluation of Response Surface Designs in Presence of Errors in Factor Levels

Abstract

Experimenters are often confronted with the problem that errors in setting factor levels cannot be measured. In the robust design scenario, the goal is to determine the design that minimizes the variability transmitted to the response from the variables’ errors. The prediction variance performance of response surface designs with errors is investigated using design efficiency and the maximum and minimum scaled prediction variance. The evaluation and comparison of response surface designs with and without errors in variables are developed for second order designs on spherical regions. The prediction variance and design efficiency results and recommendations for their use are provided.

Keywords:

• Errors in variables
• Scaled prediction variance
• Design efficiency
• Response surface design

Mathematics Subject Classification:

• Primary 62K20; Secondary 62K99