The robustness of response surface designs with errors in factor levels

ABSRTACT

Since errors in factor levels affect the traditional statistical properties of response surface designs, an important question to consider is robustness of design to errors. However, when the actual design could be observed in the experimental settings, its optimality and prediction are of interest. Various numerical and graphical methods are useful tools for understanding the behavior of the designs. The D- and G-efficiencies and the fraction of design space plot are adapted to assess second-order response surface designs where the predictor variables are disturbed by a random error. Our study shows that the D-efficiencies of the competing designs are considerably low for big variance of the error, while the G-efficiencies are quite good. Fraction of design space plots display the distribution of the scaled prediction variance through the design space with and without errors in factor levels. The robustness of experimental designs against factor errors is explored through comparative study. The construction and use of the D- and G-efficiencies and the fraction of design space plots are demonstrated with several examples of different designs with errors.

Keywords:

• Fraction of design space plot
• scaled prediction variance
• response surface design
• errors in factor levels

Acknowledgments

The authors are grateful to Bill Woodall for his useful comments and suggestions. This research was supported by National Key R&D Program of China under Grant Nos. 2016QY02D0301 and 71871204, Natural Science Foundation of China (NSFC) with Grant No. 71301117, 71302016, 81573825, 17YJC840046 and the Youth Foundation of the Ministry of Education under Grant No. 18YJC630029.