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Split-plot designs with general minimum lower-order confounding. (English) Zbl 1189.62124
Summary: Split-plot designs have been widely used in industrial experiments. Up to now, most methods for choosing this kind of designs are based on the minimum aberration (MA) criterion. Recently, by introducing a new pattern, called aliased effect-number pattern (AENP), R. Zhang et al. [Stat. Sin. 18, No. 4, 1689–1705 (2008; Zbl 1255.62223)] proposed a general minimum lower-order confounding (denoted by GMC for short) criterion and established a general minimum confounding (also denoted by GMC for saving notations) theory. It is proved that the GMC criterion selects optimal designs in a more elaborate manner than the existing ones, and when an experimenter has a prior about the importance ordering of factors in experiments the GMC designs are better than other optimal designs. We extend the GMC criterion to the split-plot design case and give a GMC-FFSP criterion for ranking split-plot designs. Some comparisons of the new criterion with the MA-MSA-FFSP criterion are given, and the optimal 32-run split-plot designs up to 14 factors under the two criteria are tabulated for comparison and application.

##### MSC:
 62K05 Optimal statistical designs 62K15 Factorial statistical designs 65C60 Computational problems in statistics (MSC2010) 62Q05 Statistical tables
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