On The Construction Of Nested Orthogonal Arrays

With the continuous development of science and technology and the improvement of productivity and production mode,more and more factors are involved in the experiment,and the relationship between factors is more and more complex.Therefore,the traditional physical experiment is time-consuming,laborious,and costly,and some fields can not be experimented at all.With the continuous progress of computer technology,in order to better study the relationship between complex things,the emergence of computer experiments attracted the eyes of statisticians.Computer experiments are widely used in the fields of commercial,engineering and scientific research for its low cost,cheap,artificial and other characteristics.But computer experiments also have drawbacks,and the most fatal disadvantage is that the accuracy of computer experiments without physical experiments is high.The double precision experiment model combines the advantages of low cost of computer experiment and high accuracy of solid experiment.It has been favored by scholars from all walks of life.The double precision model is a combination experiment model of low precision experiment and high-precision experiment,or it can be simply understood as a combination experiment of computer experiment and solid experiment.The orthogonal arrays is used to arrange the orthogonal arrays experiment.Therefore,the nested orthogonal arrays used to arrange the double precision experiment have also been sought after by the majority of scholars.However,there are relatively few studies on nested orthogonal arrays at present,but many methods of constructing orthogonal arrays can be used to construct nested orthogonal arrays.Therefore,on the basis of the method of constructing the orthogonal arrays,some methods of constructing the nested orthogonal arrays are given in combination with the research results of the predecessors.The aim of this paper is to obtain more nested orthogonal arrays to provide a theoretical basis for the double precision experiment model.The main structure of this article is as follows:The first chapter introduces some related background as well as the research status at home and abroad.The second chapter reviews the relevant concepts and the related lemmas to be used in the latter.In the third chapter,a method of constructing the nested orthogonal arrays is provided and a series of symmetric nested orthogonal arrays are given.The fourth chapter is an asymmetric nested orthogonal arrays based on the third chapter.The fifth chapter is the summary of this article and some related questions for readers to think and solve.