Construction of Mixed-level Supersaturated Designs by the Substitution Method

Supersaturated design (SSD) has received much interest because of its potential in factor screening experiments. Most studies focus on the construction and analysis of symmetrical SSDs. This paper considers the construction of asymmetrical (or mixed-level) SSDs. A new construction method, called the substitution method, for E(fNOD ) optimal and nearly-optimal SSDs is proposed. The basic idea of this method is to divide the rows of one design into several blocks, and then substitute the levels of another design with these blocks. The two designs can be SSDs and saturated orthogonal arrays, and their selections are investigated in detail. The properties of the designs generated are also discussed, and many new designs are tabulated for practical use.