ORTHOGONAL ARRAYS OBTAINED BY ORTHOGONAL DECOMPOSITION OF PROJECTION MATRICES

Abstract: This paper studies a relationship between orthogonal arrays and orthogonal decompositions of projection matrices. This relation is used for the construction of orthogonal arrays. As an application of the method, some new mixed-level orthogonal arrays of run size 36 are constructed

Satisfactory orthogonal array and its checking method

An orthogonal array (OA) is said to be a satisfactory orthogonal array if it is impossible to obtain another OA from it by adding one or more columns. By exploring the relationship between OAs and orthogonal decompositions of projection matrices, we present a method of checking a satisfactory OA.Projection matrix Satisfactory orthogonal array

Further results on the orthogonal arrays obtained by generalized Hadamard product

By combining generalized Hadamard product with difference matrix and exploring the relationship between orthogonal arrays and decomposition of projection matrix, we furthermore develop the method in Zhang et al. (Discrete Math. 238 (2001) 151). As an application of it, some new orthogonal arrays of run size 100 are constructed.Mixed-level orthogonal array Generalized Hadamard product Difference matrix Projection matrix

Normal mixed difference matrix and the construction of orthogonal arrays

We present the definitions of normal orthogonal array (OA) and normal mixed difference matrix and extend the mixed difference matrix method introduced by Wang (Statist. Probab. Lett. 28, 121). Some new mixed-level OAs are constructed through the generalized Kronecker sum of (nonorthogonal) mixed-level matrix and normal mixed difference matrices.Mixed orthogonal array Mixed difference matrix Normal mixed difference matrix Generalized Kronecker sum

A note on orthogonal arrays obtained by orthogonal decomposition of projection matrices

A method of constructing mixed-level orthogonal arrays is presented by Zhang et al. (Statist. Sinica 2, 595). It is somewhat difficult to use this method to obtain new orthogonal arrays. This paper illustrates with examples the application of the method. Several classes of mixed-level orthogonal arrays are obtained.Mixed-level orthogonal array Projection matrix Permutation matrix