  Complete reliance on the fitted model in response surface experiments is
risky and relaxing this assumption, whether out of necessity or intentionally,
requires an experimenter to account for multiple conflicting objectives. This
work provides a methodological framework of a compound optimality criterion
comprising elementary criteria responsible for: (i) the quality of the
confidence region-based inference to be done using the fitted model
(DP-/LP-optimality); (ii) improving the ability to test for the lack-of-fit
from specified potential model contamination in the form of extra polynomial
terms; and (iii) simultaneous minimisation of the variance and bias of the
fitted model parameters arising from this misspecification. The latter two
components have been newly developed in accordance with the model-independent
'pure error' approach to the error estimation. The compound criteria and design
construction were adapted to restricted randomisation frameworks: blocked and
multistratum experiments, where the stratum-by-stratum approach was adopted. A
point-exchange algorithm was employed for searching for nearly optimal designs.
The theoretical work is accompanied by one real and two illustrative examples
to explore the relationship patterns among the individual components and
characteristics of the optimal designs, demonstrating the attainable
compromises across the competing objectives and driving some general practical
recommendations.
