Asymmetric Space Filling Design

With the rapid development of computer technology,some solid experiments can be simu-lated by complex computer programs.There is no random error in computer test.In computer experiments,the response is determined for a given set of input values.Therefore,the traditional experimental design criteria,namely randomization,zoning and repetition,are no longer applica-ble in the design and analysis of computer experiments.For example,a complex time-consuming computer program like finite element analysis model can be divided into different precision to im-plement,which produces a computer test with multiple accuracy.Usually,a high-precision?time consuming?computer test and a low accuracy?Fast Computing?computer test are used to study complex solid systems.The observations obtained from this experiment are usually used to con-struct statistical models to predict the most accurate response of the test.Effective data collection is critical to the implementation of such trials.Qian et al.[42]presents a new design for computer experiments with high accuracy and low precision,called nested space filling design.Considering k different accuracy of the computer test,the response is y₁,...,y_k,where y₁comes from the highest accuracy of the test,y₂comes from second high-precision experiments,and so on.Let D₁,...,D_k represent the design matrix of the K test.Then,D₁,...,D_kusually meet the following conditions:?1?nested structures:D₁???D₂???...???D_k;?2?space filled properties:each D_iis space filled design.The orthogonal array is essential in the field of experimental design,so it is a good subject to construct a nested orthogonal table with good properties.At present,there is only one other work to construct nested orthogonal arrays.At the same time,compared with symmetric orthogonal arrays,asymmetric orthogonal arrays are more flexible and practical,which lead to the study of their construction methods.Because of its good properties,it is often used in quality control and product improvement in industrial test.Since the asymmetric orthogonal table self;Rao[46]was formally put forward,its theoretical research has always been a concern in the experimental design.The asymmetric orthogonal arrays with intensity of 2 have been extensively studied,but the study of the asymmetric orthogonal arrays with intensity greater than 2 has been relatively few.Suen et al.[49]in the paper presents a method to construct an arbitrary intensity of non symmetric orthogonal table.This paper will use the method to construct some new strength more than 2non symmetrical orthogonal table,and this method is extended,non symmetric orthogonal table to obtain a series of new nested type.In this paper,the construction method of nested orthogonal array for multi precision com-puter test is given,and the design is asymmetric orthogonal table.In addition,for a computer experiment,it is assumed that its variables are quantitative.However,a computer test may involve both qualitative and quantitative variables.The patch space filling design proposed by Qian et al.[43]is a good choice for computer experiments that contain both qualitative and quantitative variables.Each piece of space filling design corresponds to a horizontal combination of qualitative factors,and all of them should have space filling property in low dimension.Qian[39]constructs a piecewise orthogonal table with one dimensional projective uniformity.Orthogonality is an impor-tant property of space filling design.At present,Sun et al.[54]give several methods to construct nested orthogonal arrays and piecewise orthogonal arrays.On the basis of their research,this method is extended to the asymmetric case,and a series of nested asymmetric orthogonal arrays and sliced asymmetric orthogonal arrays are obtained.The details are as follows:Chapter one introduces the research background and current situation of this paper.The second chapter introduces some basic concepts,symbols and lemmas used in the following chapters.And use the construction method proposed by[54]in Sun et al.based on the calculation process and obtained a series of strength for type 3 nested asymmetric orthogonal arrays and sliced asymmetric orthogonal arrays,and at the end of this chapter is constructed a kind of strength nested 4;asymmetric orthogonal arrays and sliced asymmetric orthogonal arrays,the tectonic process than Suen et al.[50]more directly.The third chapter presents two kinds of new construction method,a method is directed by Suen et al.[49]are used to construct a non symmetric matrix C orthogonal array to obtain the new asymmetric orthogonal array,and then according to Sun et al.[54],we acquire the basic structure of nested given orthogonal array method and sheet type orthogonal array on constructing nested asymmetric orthogonal arrays and slice type non symmetric orthogonal arrays.Another method is to obtain nested asymmetric orthogonal array and sliced asymmetric orthogonal array by the existing asymmetric orthogonal arrays.And use the two methods to construct some suitable for arbitrary strength,nested g;asymmetric orthogonal arrays and sliced asymmetric orthogonal arrays,and through the examples to illustrate this,while still at the end of this chapter,we construct some tight nested asymmetric orthogonal arrays and sliced asymmetric orthogonal arrays.In the fourth chapter,the application of asymmetric orthogonal arrays and piecewise asymmet-ric orthogonal arrays in medical field is given with practical examples,and the related application of medical statistical software is involved.The fifth chapter gives the application of computer experiment in medical field combined with practical examples,and involves related applications of medical statistics software.The sixth chapter summarizes the paper and proposes some suggestions and problems to be solved.