On The Construction Of Three Level Regular GMC Designs And Asymmetric Orthogonal Arrays

In experimental designs,the experiment which all level combinations are tested the same number of times is called comprehensive experiment,and its design is called complete factorial design.In practical experimental designs,the number of level combinations increases rapidly as the number of factors or levels increases.From the perspective of practicability and economy,the fractional factorial plans,which are subsets or parts of complete factorial designs,are usually adopted when the number of factors or levels reaches a certain value.In order to ensure the efficiency of the experiment,the key is how to select the optimal design.The general minimum lower order confounding(GMC)criterion is a good criterion for selecting designs when the experimenter has prior information about the order of the importance of the factors.This paper considers the construction of three level regular fractional factorial designs under the GMC criterion.Based on the idea of complementary designs,we prove that some large three level regular designs can be obtained by combining some small resolution IV designs .We construct all the results of the small designs with the number of factors at [4,20],and tabulate them in the table.The orthogonal arrays occupy the prominent position in factorial designs.Orthogonal arrays are divided into symmetric orthogonal arrays and asymmetric orthogonal arrays.Orthogonal arrays with strength greater than 2 are called high strength orthogonal arrays.Compared to symmetric orthogonal arrays,asymmetric orthogonal arrays are very useful in theoretical studies and practical applications.However,it is difficult to construct such designs of high strength.Among the available method for constructing such designs,the method of generator matrix is particularly prominent appeal as well as its good properties.Firstly,this paper presents a general method of generator matrix for constructing asymmetric orthogonal arrays,and constructs a family of asymmetric orthogonal arrays via the method.Then we combine the general replacement procedure and further replacement procedure respectively to obtain some new families of asymmetric orthogonal arrays.