Add The Orthogonality And Structure Of The Sequential Experiment

Experiment is one of the most common activities of human beings.It's planned activities for discovering new phenomena,things,and laws.Experimenters can change the level of the factors in a system to obtain the effect of the system under different states.The goal of the experimental design is to find the optimal selection of the factor level to make the response optimal by comparing the effects of the system under different states.The order-of-addition experiment is very important in production and life,like the processing of food,the production of industrial raw materials,the addition of chemical reagents,etc.Suppose an experiment involvcs m components,The goal of the order-of-addition experiment is to find the optimal order-of-addition of the m components to optimize the response.This thesis studies the orthogonality of pair-wise ordering design and the construction of the order-of-addition design.Firstly,the development and definition of experimental design and ordcr-of-addition experiment are introduced.Then it gives the definitions and properties of algebraic orthogonality and combinatorial orthogonality of the experimental design,the proportional combinatorial orthogonality of the pair-wise ordering design.What's more,an alphabetic representation is given to represent the pair-wise ordering full design.The orthogonality of the pair-wise ordering full design is studied based on the alphabetical representation.It extends the results of the proportional combinatorial orthogonality of 4 components in Voelkel(2019)to m components.The conclusion that the interaction effect involving two pair-wise ordering factors with a common component and any main effect is algebraic orthogonal in Mee(2017),is extends to that any odd columns of pair-wise ordering full design with m components are orthogonal.Voelkel(2019)used the ?2 criterion to explain that when the pair-wise ordering design is proportional combinatorial orthogonal,the order-of-addition design has the 3 tuples with the same number of repetitions.This thesis defines the type matrix T,the T-P combination design and then gives the theoretical construction method of the order-of-addition design with 6-rows in which each 3 tuple repeats 1 time when m-4.