A commonly occurring problem in response surface methodology is that of inconsistencies in the response variable. These inconsistencies, or maverick observations, are referred to here as outliers. Many models exist for describing these outliers. Two of these models, the mean shift and the variance inflation outlier models, are employed in this research. Several criteria are developed for determining when the outlying observation is detrimental to the analysis. These criteria all lead to the same condition which is used to develop statistical tests of the null hypothesis that the outlier is not detrimental to the analysis. These results are extended to the multiple outlier case for both models. The robustness of response surface designs is also investigated. Robustness to outliers, missing data and errors in control are examined for first order models. The orthogonal designs with large second moments, such as the 2ᵏ factorial designs, are optimal in all three cases. In the second order case, robustness to outliers and to missing data are examined. Optimal design parameters are obtained by computer for the central composite, Box-Behnken, hybrid, small composite and equiradial designs. Similar results are seen for both robustness to outliers and to missing data. The central composite turns out to be the optimal design type and of the two economical design types the small composite is preferred to the hybrid. / Ph. D.