  In practice, optimal screening designs for arbitrary run sizes are
traditionally generated using the D-criterion with factor settings fixed at +/-
1, even when considering continuous factors with levels in [-1, 1]. This paper
identifies cases of undesirable estimation variance properties for such
D-optimal designs and argues that generally A-optimal designs tend to push
variances closer to their minimum possible value. New insights about the
behavior of the criteria are found through a study of their respective
coordinate-exchange formulas. The study confirms the existence of D-optimal
designs comprised only of settings +/- 1 for both main effect and interaction
models for blocked and un-blocked experiments. Scenarios are also identified
for which arbitrary manipulation of a coordinate between [-1, 1] leads to
infinitely many D-optimal designs each having different variance properties.
For the same conditions, the A-criterion is shown to have a unique optimal
coordinate value for improvement. We also compare Bayesian version of the A-
and D-criteria in how they balance minimization of estimation variance and
bias. Multiple examples of screening designs are considered for various models
under Bayesian and non-Bayesian versions of the A- and D-criteria.
