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Split-plot designs with mirror image pairs as sub-plots. (English) Zbl 1235.62110
Summary: We investigate two-level split-plot designs where the sub-plots consist of only two mirror image trials. Assuming third and higher order interactions negligible, we show that these designs divide the estimated effects into two orthogonal subspaces, separating sub-plot main effects and sub-plot by whole-plot interactions from the rest. Further we show how to construct split-plot designs of projectivity \(P\geq 3\). We also introduce a new class of split-plot designs with mirror image pairs constructed from non-geometric R.L. Plackett and J.P. Burman designs [Biometrika 33, 305–325 (1946; Zbl 0063.06274)]. The design properties of such designs are very appealing with effects of major interest free from full aliasing assuming that third and higher order interactions are negligible.

MSC:
62K15 Factorial statistical designs
62P30 Applications of statistics in engineering and industry; control charts
62K99 Design of statistical experiments
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