Multistratum fractional factorial designs

Recent work on multistratum fractional factorial designs is set in a general and unified framework, and a criterion for selecting multistratum fractional factorial designs that takes stratum variances into account is proposed. Application of the general theory is illustrated on designs of experiments with multiple processing stages, including split-lot designs, blocked strip-plot designs, and post-fractionated strip-block designs. In particular, this helps elucidate the relationship between the three different design settings studied by Miller (1997), Bingham et al. (2008), and Vivacqua and Bisgaard (2009). The construction and selection of two-stage designs in these settings are shown to be equivalent. Good designs based on our criterion are found and compared with those tabulated in Vivacqua and Bisgaard (2009).