Optimal Compromise Designs And Their Constructions

Fractional factorial design has been widely used in industry, agriculture, clinic trails, socioeconomics and many other scientific fields. For different experiments, ex-perimenters have their different purposes and need different kinds of optimal designs to carry out. Particularly, in many of them the experimenters often aim to estimate some specified factor effects and need special optimal designs for their experiments.Addelman[1] first studied a range of designs as a compromise between orthogonal main-effect designs and those permitting uncorrelated estimation of all main effects and all two-factor interactions ?2fi's?, and called them compromise designs. That paper discussed three classes of two-level compromise designs classified by estimating all main effects and three classes of specified 2fi's. Later on, Sun[45]proposed the forth one. The four classes were distinguished by the following four classes of different specified 2fi's to be estimated:1. {G₁ × G₁}, 2. {G₁ × G₁, G₂ × G₂}, 3.{G₁ ×G₁, G₁ × G₂}, 4. {G₁ × G₂},where {G₁, G₂} is a partition of the n factors in an experiment and Gi ×Gj denotes the set of 2fi's between the factors in G, and those in Gj ?i, j = 1,2?.On the basis of the background below, this thesis introduces the research of opti-mal compromise designs and their constructions. Concretely, we accomplish the fol-lowing in our work:? We call a design which can estimate any set of specified effects a compromise design and seek the optimal ones under a weaker assumption that all the forth or higher order effects are negligible. And we extend the specified effect sets as follows. We use G₁ and Gi × Gj respectively to denote the specified main effects and specified 2fi's. Similarly, we propose to study four classes of extended compromise designs and use the four sets of specified effects to respectively denote them:1.{G₁,G₁×G₁}, 2.{G₁,G₁×G₁,G₂×G₂}, 3.{G₁,G₁×G₁,G₁×G₂},4.{G₁,G₁×G₂}.? In this thesis,to assess compromise designs with the extension,a measure called partial aliased effect number pattern ?P-AENP? is introduced. And we apply the generalized variable resolution design[36] to study four classes of clear and strongly clear compromise plans and their constructions.? By the applications of variable resolution designs and generalized variable resolu-tion designs, we derive some necessary conditions for the existence of four classes of two-level strongly clear compromise designs and give some methods for con-structing strongly clear compromise designs.