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Variance Analysis of Orthogonal Experimental Design

Author: LiuMingLei
Tutor: XuWenKe
School: Northeast Forestry University
Course: Applied Mathematics
Keywords: Generalized Inverse Analysis of Variance Effect matrix Error array
CLC: O212.6
Type: Master's thesis
Year: 2011
Downloads: 621
Quote: 1
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Abstract


Experimental design (experimental design), including the three basic elements of the processing factors, subjects and treatment effects. Trial design must be followed to repeat, random and partial control of the three principles. The experimental design methods generally contrast design, randomized block design, split-plot design, orthogonal design. The trial design is one of the methods of the contemporary engineering and technical personnel must master the technology. Save a lot of manpower, material and financial resources and the time when the need to solve the multi-factor multi-level complex test, in order to reduce the number of trials, and, more importantly, the correct good test designed to reduce experimental error and improve the accuracy of the experimental a true and reliable test data, and draw the correct inference and conclusion to lay the foundation for the statistical analysis. Orthogonal experimental design is to have the ability to solve this problem. This paper attempts orthogonal experimental design analysis of variance reasonable conclusion deduced by matrix algebra as well as knowledge of the current model. Generalized inverse matrix algebra and linear model parameter estimation, multiple regression analysis model parameter estimation and hypothesis testing involved in the orthogonal experimental design to give the corresponding least squares estimation of the parameters on the overall analysis of variance, and best linear unbiased estimator. The regression coefficients in the structure of the assumptions of the test statistic, and variance analysis some parameters hypothesis test statistic given a reasonable conclusion. Papers are given in the model optimized based on, defines a class of factor effect matrix, and the matrix effect simulation test of the orthogonal test factors. Finally, an example in the orthogonal experimental design analysis of variance given specific steps as well as conclusions integrity. In the derivation of model fitting, given the focus in this article there is a linear relationship for the orthogonal experiment with two goals, how to deal with the method. Using this method results into a more rational analysis of variance model. For the the optimality definition of orthogonal experiment optimality of the orthogonal table structure, this paper given in the literature, briefly proved the necessary and sufficient conditions of optimality. Obviously, different models by actual problem, the problem comes down to a different model, and its processing different methods can be used, given for the problems which exist relatively simple processing methods. Model variables with non-linear or more complex relationship problems treatment may become relatively complex, which also can be used as a follow-up study of a subject.

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CLC: > Mathematical sciences and chemical > Mathematics > Probability Theory and Mathematical Statistics > Mathematical Statistics > Test analysis and experimental design
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