The New Conclusion Of 100 Run Mixed Orthogonal Arrays

Experiments are quite necessary in the industrial and agriculture production andscientific research. Of all the experimental methods, orthogonal experimental design isthe most popular one, which is arranged according to orthogonal arrays. The research oforthogonal arrays has been strengthened in the past decades.Orthogonal arrays are widely used with its simple and natural definition and elegantforms. There are lots of methods to constrct orthogonal arrays, in which Matrix ImageConstruction method can be used to generate new orthogonal arrays via old ones. Thismethod is first to decompose a projection matrix, which is the matrix image of a tightarray, into the sum of several orthogonal projection matrices. Then we can construct anorthogonal array with a large number of columns by piecing together several orthogonalarrays with smaller numbers of columns which have matrix images less than or equal to thecorresponding orthogonal projection matrices. This paper tries to list out all the 100-runorthogonal arrays, and most of them can be constructed by this method. Replacementmethods are useful in the constructing of the proper arrays, we will give some examples.In addition , we will introduce the algorithm to search for new mixed orthogonal arrays,which can help us to get some new orthogonal arrays. In the end, we will give the newmixed orthogonal arrays which we get through the generalized di?erence matrix, and givea new conclusion of the 100 run orthogonal arrays. The details are as follows:Chapter one is to introduce the background and current research of orthogonal arraysand some basic knowledge of this paper.Chapter two is to introduce some cases of the construction of 100-run orthogonalarrays , and the search algorithm which can get new mixed orthogonal arrays.Chapter three is to show the new 100 run mixed orthogonal array we get, and givethe new conclusion of the 100 run mixed orthogonal arrays.