The Information Theory Models Of DOE About Optimization Experiments And Explore Experiments

DOE plays an important role in the productions and daily life, in many cases we only know how to use some methods, but does not know why to be so. The authors only use some methods to get some results in most literatures, while there is little or no explanations in the area of rationality. This paper discusses some of the methods (such as bisection, secant method, symmetric truncated method, orthogonal design, uniform design) in DOE, tries to do some research on DOE from the perspective of information theory, with a wish to give reasonable explanations about these methods.First, this paper introduced some knowledge of DOE and information theory, then proposed the purposes of this paper.In the second chapter, this paper discussed some of the single factor Optimization Experiments, established the information theory models of dichotomy, secant method and optimization method, and finally established the information theory models of explore experiments of the discrete case and continuous case.In the third Chapter, this paper first introduced the knowledge of orthogonal design, then established information theory models of multi-factor multi-level(equal levels experiments) without interaction and with interaction from specific to general, When using an orthogonal design could get the same amount of information as using a full-scale experiment in the case of no interaction. In this sense, that the outcome of orthogonal design is approximate to the optimal solution. In the case of Interacting, using a full-scale orthogonal design is equal to do a full-scale experiment. In part-scale experiment, the amount of information is less than a full-scale experiment, we can not determine whether the outcome of the experiment is approximate to the optimal solution.In the fourth Chapter, this paper first introduced the knowledge of uniform design, then established information theory models of multi-factor multi-level(equal levels experiments) without interaction and with interaction, using the same methods as chapter three, but greatly reduces the number of tests. In the case of Interacting, the information of using a uniform design was much less than a full-scale experiment, so we can not determine whether the outcome of the experiment is approximate to the optimal solution. Finally, this paper did some comparison between orthogonal designs and uniform design. In the case of no interaction, orthogonal design is equivalent to doing a repeat test, and a uniform design is only do a test at each level, so the uniform design had advantages in terms of reducing the number of tests. In the case of interacting, they could neither get the total amount of information, so we can not determine whether each outcome of the two experiments is approximate to the optimal solution. But the amount of information of orthogonal design is more than uniform design, so it should give priority to the orthogonal design. In many trials of experiments, orthogonal designs are superior to uniform designs from the terms of neat comparability and mean optimal solution.