The Statistical Analysis Of Orthonogal Saturated Effects Model

There are many matured solutions to the statistic analysis of two-level orthogonal saturated designs under the assumption of "Pareto Principle" . But the "Pareto Principle" does not always work, so it is necessary to find some effective statistic methods to common saturated designs. To solve the problem, the dissertation makes two new statistic analysis methods.The dissertation is divided into six chapters.Chapter One is an introduction. It describes the common model of saturated designs, and makes a brief introduction to three typical statistic methods of saturated designs. They are half-normal plot, Lenth method, MaxU_Î¥ method. Then it analysis their application scopes and their advantages and disadvantages.Chapter Two is a study of orthogonal saturated designs that satisfy n > m + 1(n is the line mark of orthogonal arrays or the experiment run; m is the number of factors considered, the level number j is p_j(j = 1, ... , m.)). Under the assumption of "Pareto Principle" is neglected, the studies provide a new effective statistic methods to orthogonal saturated designs, that is, the statistic analysis is made with non-central F statistic, but this method can not be used in two-level orthogonal saturated designs.Chapter Three is a representation of a new statistic analysis method based on two-level orthogonal saturated designs under the assumption of "Pareto Principle" is neglected. The method is named the Procedure of Searching Zero effects. The method can solve orthogonal saturated designs with less than m significant factors (m is the total numbers of factors considered). Then it is applied to orthogonal saturated designs satisfied n > m + 1, that is multi-level orthogonal saturated designs.Chapter Four is an introduction of a new experiment design named orthogonal balanced block designs D_b×k(v). Then it shows balanced block orthogonal arrays GL_n(b¹v₁... v_m) by using balanced block designs D_b×k^t(v_t)(t = 1, ... , m.) and its relative property.Chapter Five is an introduction of a statistic mode that can be applied in the analysis of the results by GL_n(b¹v₁... v_m). Then it is about the Least Squares Estimation of unknown parameters and their property. Furthermore, it introduces the sum of squares decomposition of the model.Chapter Six is a study of saturated and unsaturated cases conducted by GL_n(b¹v₁...v_m). A satisfied result has been obtained by the application of the non-central F statistic analysis method and the Procedure of Searching Zero effects in saturated orthogonal balanced blockdesigns.