The Superiority Of The Orthogonal Design

When we talk about the superiority of the experimental design,we always hypotheses the system function for the model.And then at the basis of the system function,we look for the estimable conditions of the parameter and the optimality conditions of the design.But there are always a problem that if the hypothesis of the system function is not true,whether the conclusions on the basis of the system function is true. Of course,the answer is no. So how can we find the optimum design if we don't hypotheses the system function.In other words,can we find a distinguish method for the superiority of the design that is only relevant to the design but to the system function?In the Chapter 2,the system function for the general model is orthogonally decom-posed with the higher infinite quantity neglected.Because the Optimum design is the feasible design firstly.We in the Chapter 3 show the necessary and sufficient condition of the feasible design.The condition denoted by the matrix image is relevant to the de-sign,but to the model.The Chapter 4 is the main theorem and the main conclusion.We will prove that the orthogonal design is A-optimum.And the distinguish method is also relevant to the design,but to the system function.In this way,the problem is solved.