Generalized E(s 2) Criterion for Multilevel Supersaturated Designs

Several extensions of the popular E(s ²) criterion of Booth and Cox (1962 Booth , K. H. V. , Cox , D. R. ( 1962 ). Some systematic supersaturated designs . Technometrics 4 : 489 – 495 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) to multilevel supersaturated designs have been advanced in literature. These extensions are not unique due to different ways they measure overall nonorthogonality between all pairs of the columns of the model matrix. We exploit the connection of the E(s ²) criterion with A- and D-optimality that naturally lends itself to a generalized criterion for the multilevel situation in a unified way. The extensions provided in literature follow as special cases of the generalized criterion. A lower bound to the generalized criterion is derived for a wide class of designs, and a method of construction for the symmetrical case is discussed.