Construction and analysis of Es2Es2 efficient supersaturated designs

In this paper, we construct supersaturated designs for large numbers of two-level factors and 10⩽n⩽2210⩽n⩽22 runs by augmenting k-circulant designs [Liu, Y., Dean, A.M., 2004. k-circulant supersaturated designs. Technometrics 46, 32–43] with interaction columns or by deleting columns from k  -circulant designs. Most of the designs presented have Es2Es2 efficiencies above 0.90 and they extend the range of efficient supersaturated designs available in the literature.Difficulties encountered in the use of supersaturated designs in detecting active factors are addressed. We show that, when only one factor is active, the regression technique of forward selection is guaranteed to select the correct factor as active under the idealized conditions that non-active factors have negligible effects and the errors are small. Under similar conditions, we derive bounds on the maximum allowable correlation between the columns of the model matrix that guarantee the correct selection of the “most active” factor when two or more factors are non-negligible. Further, we obtain conditions for the correct selection of the two most active factors using subset selection in regression. A number of designs that satisfy these conditions are identified.