Supersaturated Designs for Asymmetrical Factorial Experiments

This article describes a general method of construction of supersaturated designs for asymmetric factorials obtained by exploiting the concept of resolvable orthogonal arrays and Hadamard matrices. The supersaturated design constructed here has a restricted form of t.qζ ∥ n, where ζ factors are at q-levels each and one factor is at t-levels and the number of runs is n. The designs obtained have the factor at t-levels always orthogonal to the ζ factors with q levels each in the symmetric design qζ ∥ n. The method of construction is illustrated with the help of examples. A catalogue of designs obtained is prepared and fNOD-efficiency and χ2-efficiency of the designs are given. Many designs are optimal while other designs have high efficiencies. The efficiency of the resulting design is better than that of the symmetric design qζ ∥ n.