Study On The Method Of Constructing Mixed Horizontal Fracture With More Pure Effect

Fractional factorial (FF) designs are commonly used for factorial experiments. Clear effects is a popular optimality criterion for selecting designs. In factorial inves-tigations, especially those involving physical experiments, the levels of the factors are different probably, then we can use mixed-level designs. Such designs can be construct-ed from symmetrical designs by the method of replacement, which was first formally introduced by Addelman (1962) and developed by Wu (1989), Wu et al. (1992), He-dayat et al. (1992) and Zhang and Shao (2001). A design with n two-level factors and m four-level factors is usually denoted by 2n4m. Zhao and Zhang (2008) gave a com-plete classification of the existence of clear two-factor interaction components (2FIC) of 2n4m designs.When the levels of some factors are difficult to be changed or controlled, completely randomized designs are often abandoned in the experiments. Then it is a good selection to use fractional factorial split-plot (FFSP) designs. FFSP designs have received much attention in recent years. If there are both two-level and eight-level factors in an experiment and it is difficult to change or control the levels of some factors, a split-plot 2(n1+n2)-(k1+k2)8m design can be used.This paper considers the regular split-plot 2(n1+n2)-(k1+k2)8ω1 designs. It consists of four chapters.Chapter 1 introduces the basic definitions and notation related to FF design and FFSP design.Chapter 2 gives the upper and lower bounds on the maximum number of clear two-factor interactions in 2(n1+n2)-(k1+k2) designs with resolutions III, and gives a construc-tion method for 2(n1+n2)-(k1+k2) designs containing many clear two-factor interactions.Chapter 3 gives the upper and lower bounds on the maximum number of clear 2FICs in 2(n1+n2)-(k1+k2)8ω1 designs with resolutions III and IV. We gives a construction method for 2Ⅲ(n1+n2)-(k1+k2)8ω1 designs containing many clear 2FICs in section 3.1, and then derives the upper and lower bounds on the maximum number of clear 2FICs in the designs. Section 3.2 studies a construction method for 2Ⅳ(n1+n2)-(k1+k2)8ω1 designs containing many clear 2FICs, and then derives the upper and lower bounds on the maximum number of clear 2FICs in the designs. Section 3.3 examines the performance of the bounds we obtained above.Chapter 4 gives a brief concluding to the whole article.