Experimental design is the process of planning a study to meet the objectives of interest, and is very important in order to ensure the right type of measurements and the power to answer the research questions of interest as efficiently as possible. For obtaining maximum efficiency, many criteria have been proposed in the experimental design literature. Standard criteria were useful when the variance of independent errors are available and when that is not so, the usual criteria do not have the properties that they are intended to have. Modified criteria have defined after some modifications to the standard criteria so that the resulting designs take into account the necessity of obtaining a valid estimate of error variance for proper inferences about the parameters of the model. The modified criteria, depend on the quantiles of appropriate F-distributions for inferences, may result in quite extreme designs that do not allow any lack-of-fit checks. Finally, by using compound criteria, we construct compromise designs which are efficient in terms of the properties of the information matrix and allow pure error estimation as well as lack-of fit checking. To discriminate better between different design criteria we use the robustness properties under missing observations, different model assumptions and change in criteria. Compound designs are found as robust as standard designs in all aspect of robustness, but we have to be careful about modified criteria to use.