Supersaturated Designs for Asymmetrical Factorial Experiments

Abstract

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.q^ξ // n, where ξ 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 ξ factors with q levels each in the symmetric design q^ξ // n. The method of construction is illustrated with the help of examples. A catalogue of designs obtained is prepared and f_NOD-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 q^ξ // n.

Key Words:

• Fractional factorial plans
• Resolvable orthogonal arrays
• Hadamard matrices
• Supersaturated designs