The robustness of response surface designs with errors in factor levels |
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Authors: | Juntao Fang Zhen He Shuguang He Guodong Wang |
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Affiliation: | 1. College of Management and Economics, Tianjin University, Tianjin, China;2. School of Management, Tianjin University of Traditional Chinese Medicine, Tianjin, China;3. zhhe@tju.edu.cn;5. Department of Management Engineering, Zhengzhou University of Aeronautics, Zhengzhou |
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Abstract: | ABSRTACTSince 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. |
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Keywords: | Fraction of design space plot scaled prediction variance response surface design errors in factor levels |
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