Bounds For The Maximum Number Of Pure Two-factor Interaction Components In A Mixed-level Split-plot Design

Experimental design is widely used in many fields such as industry and agriculture,and it is an important tool for engineers and scientists in product research and process development.Factorial design is one of the very common and important experimental design methods.Full factor design can estimate the main effect and interaction of all factors,but it need too many runs,so fractional factorial design is usually adopted for the sake of economy and cost saving.In an experiment,if the levels of some factors are difficult to control or change,we often use fractional factorial split-plot design.If the numbers of levels of experimental factors are not the same,we should consider using mixed-level split-plot design.A "good" mixed-level split-plot design can greatly improve the efficiency of the experiment,which is also an important topic for many scientists in recent years.Clear effects criterion is one of the commonly used criteria to select the optimal de-signs,there are many results in regular two-level fractional factorial design.However,the mixed-level split-plot design 2(n1+n2)-(k1+k2)4wmthat contains more clear effects has not been constructed.In this thesis,by constructing 2(n1+n2)-(k1+k2)4wm design with more clear two-factor interaction components,the bounds on the maximum number of clear effects for 2(n1+n2)-(k1+k2)4mw design of resolution ? and resolution ? are obtained.For a mixed-level split-plot design 2(n1+2n)-(k1+k2)4mwwith resolution ?,it can be obtained by replac-ing from two-level fractional factorial split-plot design.This thesis first improves the con-struction method of two-level fractional factorial split-plot designs,and derives the upper and lower bounds on the maximum numbers of clear two-factor interaction components in 2(n1+n2)-(k1+k2)4mw designs.The whole-plot of a 2(n1+n2)-(k1+k2)4mw design is regarded as a mixed-level fractional factorial design 2n-k 4m with the resolution ?,and the upper bounds on the maximum numbers of clear two-factor interaction components with whole-plot are obtained.According to the number of alias sets,the upper bounds on the maximum num-bers of clear two-factor interaction components of whole-plot factor and sub-plot factor in 2(n1+n2)-(k1+k2)4mw designs are derived.The lower bounds on the maximum numbers of clear two-factor interaction components in 2(n1+n2)-(k1+k2)4mw designs are given by constructing special designs.