Uniform Design With Prior Information Of Factors Under Weighted Wrap-around L₂-discrepancy

In uniform design,it is generally assumed that all factors are equally important.According to prior information,if it is known before the experiment that some factors are important and some factors may not be important,it is unreasonable to arrange the factors in a completely random manner at this time.For example,when a certain experiment factor has prior information and shows that this factor is important,if the experiment factor is randomly arranged in the design table,this important factor may be arranged in columns of the design with many aberrations.This situation will affect the estimate of the effect of this important factor,and the estimate of the effect of other factors that are confounded with this important factor.While literature on constructing efficient experimental designs has been plentiful,how best to incorporate prior information when assigning factors to the columns of a experiment design has received little attention.In uniform design,how to add prior information of factor and how to reflect the importance of factors are of great significance to the theoretical research and application of uniform design.Based on the above considerations,this paper mainly carries out the following three aspects of work:(1)In the case that prior information of some factors is known,by assigning different weights to factors of different importance,a new concept of weighted wraparound L2-discrepancy is proposed,which can be used to measure the uniformity of design with prior information of factor.(2)In this paper,the relation between weighted wrap-around L2-discrepancy and generalized wordlength is established for two level,three level,two and three mixed level design,and the definition of weighted generalized word length is given.It can be used to describe the degree of confusion in a design with prior information.(3)The properties of weighted wrap-around L2-discrepancy are studied for two level,three level,two and three mixed level designs,and the lower bound of weighted wrap-around L2-discrepancy is obtained.The purpose of this paper is to distinguish the importance of each column in the design table and to improve the rationality of the test arrangement.The weighted wrap-around L2-discrepancy proposed in this paper can rank the importance of each column in uniform design,which has important significance for the research and application of the theoretical properties of uniform design such as foldover and projection.The weighted generalized wordlength scheme defined in this paper is only applicable to the two level,three level,two and three mixed level irregular design and can rank the importance of the columns in the design.