Systematic fractional factorial designs from cyclic codes

This article presents a novel approach that utilizes binary cyclic codes to construct two categories of systematic, nearly trend-free, run-after-run fractional 2n–p factorial designs. In these designs, all n factors {A1, A2, …, An}, except A1 and An, are orthogonal to the potential time trend that may occur between successive runs. The two categories developed are systematic half 2n–1 and quarter 2n–2 fractional factorial designs. For each design, we provide the number of factor-level changes between successive runs, the total number of factor-level changes (i.e. the experimentation cost), and the sequencing of runs based on the generalized foldover scheme (GFS) of Coster and Cheng. Additionally, the independent (n – p) GFS run generators, defining contrasts, and resolutions are detailed for each design category.