  The analysis of screening experiments is often done in two stages, starting
with factor selection via an analysis under a main effects model. The success
of this first stage is influenced by three components: (1) main effect
estimators' variances and (2) bias, and (3) the estimate of the noise variance.
Component (3) has only recently been given attention with design techniques
that ensure an unbiased estimate of the noise variance. In this paper, we
propose a design criterion based on expected confidence intervals of the first
stage analysis that balances all three components. To address model
misspecification, we propose a computationally-efficient all-subsets analysis
and a corresponding constrained design criterion based on lack-of-fit.
Scenarios found in existing design literature are revisited with our criteria
and new designs are provided that improve upon existing methods.
