Two-level screening designs derived from binary nonlinear codes

Nonregular fractional factorial designs can provide economical designs in screening experiments. In this paper, two criteria are proposed for evaluating the projectivity and uniformity properties of projections onto active factors in two-level nonregular fractional factorial designs. Moreover, two-level nonregular fractional factorial designs derived from binary nonlinear codes with 12, 24, 32 and 40 codewords and various lengths are evaluated using the new criteria. Such designs are also evaluated under the known E(s2)E(s2) criterion for optimal designs in screening experiments, and are compared to Plackett–Burman designs or to projections of Plackett–Burman designs. Results show that some binary nonlinear codes can provide useful two-level nonregular fractional factorial designs in screening experiments. A search method is proposed for finding good designs with a large number of factors, starting from a good design with the same number of runs but with a smaller number of factors.