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Sun, T. and Zhao, S. (2022), General minimum lower-order confounding three-level split-plot designs when the whole plot factors are important. Can J Statistics. https://doi.org/10.1002/cjs.11744
In a split-plot design, the factors are divided into two kinds, the whole-plot (WP) fac-tors and the subplot (SP) factors. The levels of the WP factors are difficult or expensive to change, and the levels of SP factors are relatively easy to change. The split-plot designs have the advantages of saving time or cost, so they are widely used in all walks of life, especially in industry. The authors studied the three-level regular fractional factorial split-plot (FFSP)designs with the WP factors being more important than the SP factors. Such designs are commonly used in practice. They introduced an aliased component-number pattern of type WP (WP-ACNP) for ranking three-level FFSP designs. Then, based on the WP-ACNP, they extended the general minimum low-order confounding (GMC) criterion, which is proposed considering the prior information on the importance of factors, to three-level FFSP design-s and proposed a new optimality criterion for selecting such designs, which is the general minimum low-order confounding of type WP (WP-GMC). Using a finite projective geometric formulation and taking the complementary sets as the main technical tool, they derived explicit formulae connecting the leading terms of the WP-ACNP. Based on these results, they constructed some WP-GMC FFSP designs so that experimenters can directly apply them.More Details