Construction Of A Mixed-level Split-plot Design With Pure Two-factor Interaction Components

Experiment is an important means for people to know and understand nature,which has been widely used in agriculture,industry and so on.Full design includes all level combinations of each factor,and it can estimate all the main effects and interactions of all factors.Due to the limitation of experimental cost and time,many experiments can only implement fractional factorial design.In practice,when it is very difficult or expensive to change the levels of some factors,it is impossible to carry out a completely random fractional factorial design.Then it is necessary to adopt the fractional factorial split-plot(FFSP)design to meet this special require-ment.In many experiments,because the numbers of the levels of the factors are not exactly the same,so it is necessary to use mixed-level experiment design.When the levels of some factors are difficult to change in the mixed-level experiment,mixed-level split-plot design can be considered to meet the experiment requirements.How to construct an optimal mixed-level split-plot design to achieve the most economical and eficient purpose has become the most concerned problem for the experimenter.The clear effects criterion is one of the commonly used criteria to select the optimal design.Assuming that the interaction components of three or more fac-tors can be ignored,the unbiased estimators of clear main effect components and clear two-factor interaction components can be obtained.In this paper,we mainly study the construction of 2(n1+n2)-(k1+k2)4sm design with more clear two-factor in-teraction components under the clear effects criterion,and obtain the upper and lower bounds on the maximum numbers of clear two-factor interaction components in the mixed-level split-plot designs with resolution ? or ?.Specifically,for a 2(n1+n2)-(k1+k2)4sm design with m=1,2,when the resolution is ?,we first improve the construction method of two-level FFSP designs,so as to improve the lower bounds on the maximum numbers of clear two-factor interactions for 2(n1+n2)-(k1+k2)designs with resolution ?.Then,the relationship between designs 2(n1+n2)-(k1+k2)and 2(n1+n2)-(k1+k2)49m is established by using the method of replacement,and the upper and lower bounds on the maximum numbers of clear two-factor interaction components in 2(n1+n2)-(k1+k2)4sm designs are derived.When the resolution is IV,the whole-plot of 2(n1+n2)(k1+k2)4sm design is regarded as a 2n1-k1 design,and the upper bounds on the maximum numbers of clear whole-plot and whole-plot interaction components are obtained.Then,according to the number of alias sets,the upper bounds on the maximum numbers of clear whole-plot and sub-plot interaction com-ponents of 2(n1+n2)-(k1+k2)4sm designs are derived.Finally,by constructing a special design,the lower bounds on the maximum numbers of clear whole-plot and sub-plot interaction components of 2(n1+n2)-(k1+k2)4sm designs are obtained.