Some Results On2^{（n₁+n₂）-（k₁+k₂）}4²designs Contaning Clear Effects

Fractional factorial （FF） designs are commonly used for factorial experiments. Clearefects is a popular optimality criterion for selecting designs. In factorial investigations,especially those involving physical experiments, there are often factors with four levels.Then mixed-level designs are used in the experiments. Such designs can be constructedfrom two-level designs by the method of replacement, which was first formally introducedby Addelman （1962） and developed by Wu （1989）, Wu et al.（1992）, Hedayat et al.（1992）and Zhang and Shao （2001）. A design with n two-level factors and m four-level factorsis usually denoted by2n4m. Zhao and Zhang （2008） gave a complete classification of theexistence of clear two-factor interaction components （2FIC） of2n4mdesigns.When the levels of some of the factors are difcult to be changed or controlled, it maybe impractical or even impossible to perform the experimental runs of FF designs in acompletely random order. This motivates us to use fractional factorial split-plot （FFSP）designs to meet the special demands. FFSP designs have received much attention inrecent years. If there are both two-level and four-level factors in an experiment and itis difcult to change or control the levels of some factors, a split-plot2（n1+n2）（k1+k2）4mdesign can be used.This paper considers the regular split-plot2^{（n₁+n₂）-（k₁+k₂）}4²mdesigns. It consists ofthree chapters.Chapter1introduces the basic definitions related to FF design, optimality criterionand fractional factional split-plot design.Chapter2gives a complete classfication of the2^{（n₁+n₂）-（k₁+k₂）}4²designs contain-ing various clear efects. Section2.1introduces the notations and definitions of twotypes of mixed-level fractional factorial split-plot designs,2^{（n₁+n₂）-（k₁+k₂）}4²sdesigns and2^{（n₁+n₂）-（k₁+k₂）}4²designs according to the diference of the four-level factor in WP sectionor in SP section, and gives the concepts of three types of two factor interaction compo-nents. Sections2.2and2.3, respectively, study resolution III and IV2^{（n₁+n₂）-（k₁+k₂）}4²designs and give the conditions of such designs containing various clear efects. Section 2.4gives the conditions for resolution III and IV2^{（n₁+n₂）-（k₁+k₂）}4²designs containingvarious clear efects.Chapter3gives a brief concluding to the whole article.