Some Notes On Interactions Of Mixed-Level Orthogonal Arrays

When we are doing experiment with orthogonal arrays,one class of them can be used to investigate interactions between two factors.Such as L₉(3⁴),the interaction between 1 ,2 column are 3,4 column.For the other class of them,such as L₁₂(2¹¹),L₂₀(2¹⁹),L₁₈(2¹Ã—3⁷),L₃₆(2¹¹Ã—3¹²),L₃₆(2³Ã—3¹³),we still consider that they are "uniformity separate " in other columns,the question is how to investigate "uniformity separate "? How to investigate the confounding of interactions? What is the distribution of interaction for symmetry and asymmetry arrays?Firstly,This paper review two methods of definitions for interactions have already been used.One is from the orthogonal array and the other from the function model. This paper presents the relationship between them by using the decomposition operator in theory of multilateral matrices.It's still a great difficult to deal with the problems with confounding.It the third section,this paper discuss the measurement of confounding of interactions.Pang S.Q.get a simple method of determinant of interactions of symmetry arrays.Zhou J.X.studied some interactions between two columns of some orthogonal arrays,and found that it is not "uniformity separate " of some orthogonal arrays,such as L₂₀(2¹⁹),which is commonly consider as "uniformity separate ".By using the mathematical model,decomposition operator in multi-matrix theory and the extreme nature of eigenvalue,this paper studied the interactions of mixed level orthogonal array and found 5 indexes within eigenvalue to measure it,provide a lot of examples of both symmetry and asymmetry arrays in section 3.More applied examples of outstanding confounding columns of interactions between two columns can be found in section 4.It is still displayed in the proper order of symmetry arrays and asymmetry arrays.This paper find that the tests can be invalidated while putting the factors on the confounding columns both for symmetry arrays and asymmetry arrays.