The SP-type Effect Is More Important In The GMC Theory Of Time-splitting Area Design

Fractional factorial split-plot design has been widely applied to factorial experiments.When the levels of some factors are difficult to change or changing the levels of factors costs too much,we often use fractional factorial split-plot design.The split-plot design has been widely used in industrial and agricultural trials.So far,most of the methods for selecting this design are based on the minimum aberration criterion,referred to as the MA criterion.Zhang et al.(2008)introduced a new pattern,called aliased effect-number pattern(AENP).The general minimum confounding(GMC)criterion was established.Then,the GMC criterion was compared with some existing ones,and the relationship between the GMC criterion and other criteria was studied.When the experimenter has prior information on the ordering of important factors in the experiment,the GMC design is superior to other optimal designs.Wei et al.(2010)proposed a GMC-FFSP criterion for selecting the fractional factorial design.By studying the AENP,we find that the optimal design is better in the number of estimable effects.This article will continue to study the GMC criterion for split-plot design.For the whole-plot(WP)factors and sub-plot(SP)factors of split-plot design,if we have a priori information that the SP-type effect(the effect containing at least one SP factor)is more important,we prioritize the test power of the SP-type effect,and then extend the GMC criterion to the split-plot design.By giving a new AENP,a new GMC criterion is established,which is the split,plot general minimum low-order confounding(SP-GMC)criterion that prioritizes the SP-type effect test power.Then we study the difference between the SP-GMC criterion and the GMC-FFSP criterion in comparing the optimal designs.Then,we propose the second word length of the split,plot design according to the structure of the split-plot design,and consider the test power as a priority.We give the new definition of minimum secondary aberration fractional factorial split-plot(MA-MSA-FFSP)design criterion,then we compare the SP-GMC criterion and MA-MSA-FFSP criterion through some examples,and we study the applicable environment of the SP-GMC criterion and MA-MSA-FFSP criterion.The definition of the clear effect criterion of the FFSP design is similar to the clear effect criterion of the regular two-level fractional factorial design.We have a priori information that the SP-type effects are more important,so we divide the clear two-factor interactions of split-plot design into three categories.We compare the SP-GMC criterion and the GMC-FFSP criterion by combining the test power and the clear effects,then we give some conclusions.Finally,the SP-GMC criterion is extended to the robust parameter design.In the robust parameter design,the factor effects are sorted from the two perspectives of significance and interest,respectively.Bingham and Sitter(2015)combined the split-plot design with the robust parameter design,and gave the definition of minimum aberration fractional factorial split-plot robust parameter design(MA-FFSP-RPD).Although this criterion performs well in selecting the optimal design,two non-isomorphic MA-FFSP-RPD designs cannot be ac-curately filtered.In this paper,based on the effect hierarchy principle of robust parameter design and the test power of split-plot design,a general minimum low-order confounding frac-tional factorial split-plot robust parameter design(GMC-FFSP-RPD)criterion is proposed,which is used to select the optimal fractional factorial split-plot robust parameter design.We discuss the difference between the GMC-FFSP-RPD criterion and the MA criterion.