Abstract
By using the relationship between orthogonal arrays and decompositions of projection matrices and projection matrix inequalities, we present a method for constructing a class of new orthogonal arrays which have higher percent saturations. As an application of the method, many new mixed-level orthogonal arrays of run sizes 108 and 144 are constructed.
Highlights
An n × m matrix A, having ki columns with pi levels, i =, . . . , r, m = r i= ki, pi =pj for i = j, is called an orthogonal array (OA) of strength d and size n if each n × d submatrix of A contains all possible × d row vectors with the same frequency
In the construction of new mixed orthogonal arrays, two goals should be kept in mind, first, we want the orthogonal array to be as close to a saturated main-effect plan as possible so that there will be a large number of factors and second, we want the pi, the number of levels, to be as large as possible so that the design has a high degree of flexibility
By the definition of an orthogonal array (OA), any OA of run size with two factors having three levels can contain the two columns ( ) ⊗ and ⊗ ( ) ⊗ through row permutations
Summary
3 Some examples These matrix inequalities in Theorems , , and are very useful for construction of orthogonal arrays.
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