The Structure Of A Mixed Water Split Design With Pure Effect

Fractional factorial (FF) designs are commonly used for factorial experiments.When the levels of some of the factors are difficult to be changed or controlled, itmay be impractical or even impossible to perform the experimental runs of FF designsin a completely random order. This motivates us to use fractional factorial split-plot(FFSP) designs to meet the special demands. In factorial investigations, there arenot only two level factors, but also high-level factors. If there are both two-level andfour-level factors in an experiment and it is difficult to change or control the four-levelfactors, a split-plot 2(n1+n2) (k1+k2)4Wm design can be used.Bounds on the maximum number of clear two-factor interactions for 2(n1+n2)-(k1+k2)4W1designs are considered in this paper. The thesis is divided into four sections accordingto contents.Chapter 1 introduces the basic definitions related to FF design, optimality crite-rion and fractional factional split-plot design.Chapter 2 gives bounds on the maximum number of clear two-factor interactionsfor 2(n1+n2)-(k1+k2)4W1 designs. Section 2.1 introduces the notations and definitionsof mixed-level fractional factorial split-plot designs 2(n1+n2)-(k1+k2)4W1 , and gives theconcepts of three types of two-factor interaction components. Section 2.2 and 2.3respectively gives bounds on the maximum number of clear two-factor interactions for2(n1+n2)-(k1+k2)4W1 designs of resolution Ⅲ and Ⅳ.Chapter 3 gives bounds on the maximum number of clear two-factor interactionsfor 2(n1+n2)-(k1+k2)4W1 designs. Section 3.1 gives upper bounds on the maximum numberof clear two-factor interactions for 2(n1+n2)-(k1+k2)4W1 designs. Section 3.2 gives lowerbounds on the maximum number of clear two-factor interactions for 2(n1+n2)-(k1+k2)4W1designs.Chapter 4 gives a brief concluding to the whole article.