Based On The Complement Set To Construct A 2-level MA Partition Group Design

Factorial design is commonly used in various experiments.It is often used t.o study whether experiments are significantly affected by various factors.Full design is the design of all level combinations containing all factors.The advantage of full design is that it can esti-mate all the main effects and interactions of the factors.As the number of factors increases,the number of level combinations of all factors increases rapidly.In this case,experimenter can only select a part of the full design to carry out the experiment,which is called a fractional factorial design.Fractional factorial design is usually used in all experiments.Randomization is one of the three basic principles in the design of experiments.The premise of randomization is that each experiment unit has homogeneity.In fact,some factors are difficult to control.Experimenter cannot guarantee the homogeneity of experiment units,which will lead to the increase of experiment errors and the decrease of the accuracy of the experiment results.The common method to solve such problems is to divide the experiment units into several groups,called blocks.Put the homogeneous experiment units in the same block,and the non-homogeneous experiment units in different blocks.This kind of designs are called blocked designs.The minimum aberration(MA)criterion is one of the common used criteria for selecting the optimal design.The thesis focuses on constructing 2-level optimal block designs under the MA criterion.Let Hk={1,2.12,3,13,23,123,...,k,1k,2k,...,123...k}be the sarurated design generated by k independent columns 1,2,...,k.A 2n-m:2r block design d can be represented by an ordered subsets pair(St,Sb)of Hk,denoted by d=d(St,Sb).It has 2k(k=n-m)le.vel combinations,n treatment factors,2r blocks.Let.Ai,0 and Ai,1 denote the number of treatment and block defining words of length i of design d,respectively.The thesis first reviews the effect,hierarchy principle for fractional factorial design and blocked design and the two word length patterns given in[9]unde.r this principle:W1(d)=(A3.0(d),A4,0(d),.42,1(d),A5,0(d),A6,0(d),A3,1(d),...),where Ai,1 is between A2i,0 and A2i+1,0(i?2),W2(d)=(A3.0(d),A2,1(d),A4,0(d),A5,0(d),A3,1(d),A6,0(d),...),where Ai,1 is between A2i-1,0 and A2i,0(i? 2).Designs that minimize W1 and W2 sequentially are called W1-MA design and W2-MA design,respectively.Let 2w-1?2k-1-n<2wfor some integer w(1?w?k-1).Let Hw={1,2,12,3,13,23,123,...,w,1w,2w,...,123...w}be the closed subset of Hk generated by w independent columns 1,2,...,w.When 2w-1<2k-1-n<2W,if d(St,Sb)is a W1-MA or W2-MA design,then Hw(?)St,where Hw=Hk\Hw.Let St==St\Hw.This thesis obtains the following relationships between the word length patterns of d(St,Sb)and d(St,Sb)Ai,0(St,Sb)=constant+Ai,0(St,Sb),i=3,4,5,...,n,Ai,1(St,Sb)=constant+Ai,1(St,Sb),i=2,3,...,n.Using these relationships,some rules for constructing MA designs are given.Some W1-MA and W2-MA block designs are constructed at last.