Two Classes Of Compromise Plans With Clear Two-Factor Interactions

The compromise plan has important research value because of its special structure. A two factor interaction (2fi) is clear if it is not aliased with any main effect or any other 2fi. Compromise plans are said to be clear if they have resolutionâ…£(orâ…£^- in compromise 2^m-p : 2^l plans) and all the specified 2fi's are clear. Clear compromise plans allow joint estimation of all main effects and the clear 2frs under the weak assumption that all three-factor and higher order interactions are negligible.This paper includes three chapters. Chapter 1 introduces some basic concepts, several kinds of optimality criteria, some basic symbolic representation of the fractional factorial designs, and elaboration basic philosophy and some rationale about the compromise plan.Chapter 2 mainly studies the fractional factorial blocked compromise 2^m-p : 2^l plans and discusses the existence and characteristics of clear compromise 2^m-p : 2^l plans with the resolutionâ…£andâ…£^-. Section 2.1 introduces some notations for blocked FF design. For a 2^m-p : 2^l design D = (D₀, B), divide the group D₀ of the m treatment factors into two groups, D₁= {a₁, a₂,..., a_m1} and D₂ = {a_m1+1,..., a_m}. When some specified 2fi's. say the 2frs inare clear in a design D, we call this design clear compromise plan of D₁×D₁. In Section 2.2, the necessary conditions are obtained for the existence of three classes of clear compromise 2_â…£^m-p : 2^l plans of D₁×D₁, D₁×D₁ and D₁×D₂, and D₁×D₂. And we have proved there exists no 2_â…£^m-p : 2^l clear compromise plan of D₁×D₁ and D₂×D₂. In Section 2.3, we mainly discuss the existence and characteristics of clear compromise 2_â…£^m-p : 2^l plans. The necessary conditions are obtained for the existence of each class of clear compromise 2_â…£^m-p : 2^l plans. In Chapter 3, we first introduce some basic contents and the elementary knowledge of fractional factorial split-plot designs. Then, we mainly discuss the existence and characteristics of clear compromise 2^{(n₁+n₂)-(k₁+k₂)} plans. And the necessary conditions are obtained for the existence of four classes of clear compromise 2^{(n₁+n₂)-(k₁+k₂)} plans.