  Standard optimality criteria (e.g. A-, D-optimality criterion, etc.) have
been commonly used for obtaining optimal designs. For a given statistical
model, standard criteria assume the error variance is known at the design
stage. However, in practice the error variance is estimated to make inference
about the model parameters. Modified criteria are defined as a function of the
standard criteria and the corresponding error degrees of freedom, which may
lead to extreme optimal design. Compound criteria are defined as the function
of different modified criteria and corresponding user specified weights.
Standard, modified, and compound criteria based optimal designs are obtained
for $3^3$ factorial design. Robustness properties of the optimal designs are
also compared.
