Design Of Mixed Fracture With More Pure Effect

Eractional factorial(FF)designs are commonly used for factorial experiments. Clear effects is a popular optimality criterion for selecting designs. Under the weak assumption that interactions involving three or more factors can be negligible,a clear effect can be estimated unbiasedly.In factorial investigations,especially those involv-ing physical experiments,there are often factors with four levels. Then mixed-level designs are used in the experiments.When the levels of some of the factors are difffcult 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.There are two types of factors in fractional factorial split-plot designs,the hard-to-change factors are called whole plot (WP)factors and the rest are called subplot(SP)factors.If there are both two-level and four-level factors in an experiment and it is difficult to change or control the levels of some factors,a split-plot mixed-level design containing two-level and a four-level factors can be used.This paper considers the regular split-plot 2(n1+n2)-(k1+k2)41/s designs.It consists of four chapters.Chapter 1 introduces the basic definitions related to FF design,optimality criterion and FFSP design.Chapter 2 establishes bounds on the maximum numbers of clear WP and WS two-factor interactions for 2Ⅲ(n1+n2)-(k1+k2)41/s,where a WP two-factor interactions means a two-factor interactions in which both factors are WP factors,and similarly a WS two-factor interactions means a two-factor interactions in which one factor is a WP factor and the other is an SP factor.Section 2.1 introduces the notation and definitions of 2(n1+n2)-(k1+k2)41/sdesigns,and gives the concepts of three types of two factor interaction components.Sections 2.2 provides the construction methods for 2Ⅲ(n1+n2)-(k1+k2) designs with clear two-factor interactions,and establishes upper and lower bounds on the Haximum numbers of clear WP and WS two-factor interactions for 2Ⅲ(n1+n2)-(k1+k2)41/s designs. section 2.3 studies the 2Ⅲ(n1+n2)-(k1+k2)41/s designs and gives a bound on the maximum mumbers of clear WP and WS two-factor interactions for 2Ⅲ(n1+n2)-(k1+k2)41/s designs.Section 2.4 examines the performance of the lower and upper bounds on the maximum number of clear WP and WS two-factor interactions obtained in Section 2.3.Chapter 3 establishes bounds on the maximum numbers of clear WP and WS two-factor interactions for 2Ⅳ(n1+n2)-(k1+k2)41/s:designs.Section 3.1 studies the 2Ⅳ(n1+n2)-(k1+k2)41/s designs and gives an upper bound on the maximum numbers of clear WP and WS two-factor interactions for 2Ⅳ(n1+n2)-(k1+k2)41/s designs.Section 3.2 gives a lower bound on the maximum numbers of clear WS two-factor interactions for 2Ⅳ(n1+n2)-(k1+k2)41/s designs Section 3.3 examines the performance of the lower and upper bounds on the maximum number of clear WS two-factor interactions.Chapter 4 gives a brief concluding to the whole article.