Robustness to missing observation and optimalities of response surface designs with regular and complex structure

Abstract

Most of the scientific and industrial experiments usually involve small number of factors, especially biomedical experiments and computer based experiments. We construct some highly useful designs for small number of factors. Designs are constructed using subsets of regular structure and the subsets based on irregular fractions. We compare the various designs on the basis of their robustness to missing design point under minimax loss criterion. To explore some other useful properties designs are also compared on the basis of common alphabetic optimalities. For the investigation of prediction capability of competing designs, we have constructed fraction of design space plots for the variance of difference of response. We observe that some uncommon designs reveal nicer qualities of a good design. It was interesting to see various choices of designs under different optimality criteria. Suggested designs can be highly useful for the experimenters to choose a plan possessing desirable qualities.

Keywords:

• Fraction of design space plot
• Minimax loss design
• Missing observation
• Optimality criteria
• Subset design

MATHEMATICS SUBJECT CLASSIFICATION:

• 15B30

Acknowledgments

The authors are thankful to the reviewer and the Editor in Chief for helpful comments which led to improve the article.