Mixed-level Fractional Factorial Split-plot Designs2（n₁+n₂）-（k₁+k₂）4_w¹4_s¹Containing Clear Effects

Fractional factorial (FF) designs are commonly used for factorial experiments. When the levels of some factors are difficult to be changed or controlled, it may be impractical or even impossible to perform the experimental runs of FF designs in a completely random order. This motivates us to use fractional factorial split-plot (FFSP) designs to meet the special demands. If there are both two and four-level factors in an experiment and it is difficult to change or control the levels of some factors, a split-plot2(ni+n2)-(k1+k2)4m design can be used.This paper considers the regular split-plot2(ni+n2)-(k1+k2)4ω14s1designs. It consists three chapters.Chapter1introduces the basic definitions related to FF design, optimality criterion and fractional factional split-plot design.Chapter2gives a complete classfication of the2((ni+n2)-(k1+k2)4m designs containing various clear effects. Section2.1gives a simple summary on the literature. Section2.2introduces the notations and definitions of the2(ni+n2)-(k1+k2)4ω14s1designs, and gives the concept of three types of two factor interaction components. Section2.3studies resolution Ⅲ2(ni+n2)-(k1+k2)4ω14s1designs and gives the sufficient and necessary conditions of such designs containing various clear effects. Section2.4gives the sufficient and necessary conditions for resolution Ⅳ2(ni+n2)-(k1+k2)4ω14s1, designs containing various clear two-factor interaction components.Chapter3gives a brief concluding to the whole article.