Theory & Methods: Comparison of Four New General Classes of Search Designs

A factor screening experiment identifies a few important factors from a large list of factors that potentially influence the response. If a list consists of m factors each at three levels, a design is a subset of all possible 3m runs. This paper considers the problem of finding designs with small numbers of runs, using the search linear model introduced in Srivastava (1975). The paper presents four new general classes of these ‘search designs’, each with 2m−1 runs, which permit, at most, two important factors out of m factors to be searched for and identified. The paper compares the designs for 4 ≤ m ≤ 10, using arithmetic and geometric means of the determinants, traces and maximum characteristic roots of particular matrices. Two of the designs are found to be superior in all six criteria studied. The four designs are identical for m= 3 and this design is an optimal design in the class of all search designs under the six criteria. The four designs are also identical for m= 4 under some row and column permutations.