Variance Analysis Of Orthogonal Experimental Design

Experimental design includes three basic elements-processing elements, subjects and treatment affects. Performing a design experiment must obey the three principles-repeating, randomization and the local control. The experimental design methods generally include comparision design, randomized block design, split plot design, orthogonal design and so on. Experimental design approach is one of the technical methods which are necessarily mastered by the engineers. When we need to solve the multi-factor and multi-level complex experiments, we try to reduce the number of experiment, save lots of manpower, material, financial resource and time. More importantly, correct experimental design can reduce experimental errors. improve the accuracy of experiments and obtain real and reliable experimental data, thus it could lay for the foundation the correct deduction and conclusions of statistical analysis. The orthogonal experimental design just has the ability to solve such problems.Using matrix algebra and the konwledge of the current model, we attempt to derive the reasonable conclusion from the analysis of variance in the orthogonal experimental design. Making using of the generalized inverse in matrix algebra, the parameter estimation about the linear model, and the multiple regression analysis model, hypothesis testing, we give the least squares estimation and the best linear unbiased estimation about each parameter in the overall variance analysis of orthogonal experimental design. Further more, we structure the hypothesis testing statistics for the regression coefficient in the model and give a reasionable conclusion about the parameter hypothesis test in the part of variance analysis, on the base of the optimization for the model, after defining an effect factor matrix, we have the simulation experiment about the factor offect in the orthogonal test using this matrix. Finally, the detailed steps and conclusions of the variance analysis are giver by illustrating an example in the orthogonal experiment design.This paper focuses on the method of dealing with the situation when the two goals have linear relationship in the orthogonal experiment. The research resuts could be trrned into a more reasonable model of variance analysis by our method. For the construce of the orthogonal table in the orthogonal experiment, the defination of optimality is given by literature and the proof of the necessary and sufficient condition of the optimality is obtained.Obviously, since the different problems exist in the different models, the problems could be come down to different models and the methods for solving promblems are different. This paper gives a class of relativly simple method for dealing with the problems. If there exists the nonlinear or more complex relationship between the variables in the models, it could be more difficult to deal with these problems. This will be our future work.