Complete Enumeration of Two - Level Orthogonal Arrays of Strength D with D + 2 Constraints
نویسنده
چکیده
Enumerating nonisomorphic orthogonal arrays is an important, yet very difficult, problem. Although orthogonal arrays with a specified set of parameters have been enumerated in a number of cases, general results are extremely rare. In this paper, we provide a complete solution to enumerating nonisomorphic two-level orthogonal arrays of strength d with d+ 2 constraints for any d and any run size n= λ2. Our results not only give the number of nonisomorphic orthogonal arrays for given d and n, but also provide a systematic way of explicitly constructing these arrays. Our approach to the problem is to make use of the recently developed theory of J-characteristics for fractional factorial designs. Besides the general theoretical results, the paper presents some results from applications of the theory to orthogonal arrays of strength two, three and four.
منابع مشابه
β-galactosidase Production by Aspergillus niger ATCC 9142 Using Inexpensive Substrates in Solid-State Fermentation: Optimization by Orthogonal Arrays Design
Background: Enzymatic hydrolysis of lactose is one of the most important biotechnological processes in the food industry, which is accomplished by enzyme β-galactosidase (β-gal, β-D-galactoside galactohydrolase, EC 3.2.1.23), trivial called lactase. Orthogonal arrays design is an appropriate option for the optimization of biotechnological processes for the production of microbial...
متن کاملEnumeration of binary orthogonal arrays of strength 1
A k2m×n (0,1) matrix is called a binary orthogonal array of strength m if in any m columns of the matrix every one of the possible 2 ordered (0,1) m-tuples occurs in exactly k rows and no two rows are identical. In this paper, the enumeration of binary orthogonal arrays is studied, and a closed expression for the enumeration of binary orthogonal arrays of strength 1 is given using the inclusion...
متن کاملEnumeration of Strength 3 Mixed Orthogonal Arrays
We introduce methods for enumerating mixed orthogonal arrays of strength 3. We determine almost all mixed orthogonal arrays of strength 3 with run size up to 100.
متن کاملOn the optimal correction of inconsistent matrix equations $AX = B$ and $XC = D$ with orthogonal constraint
This work focuses on the correction of both the coecient and the right hand side matrices of the inconsistent matrix equations $AX = B$ and $XC = D$ with orthogonal constraint. By optimal correction approach, a general representation of the orthogonal solution is obtained. This method is tested on two examples to show that the optimal correction is eective and highly accurate.
متن کاملAffine designs and linear orthogonal arrays
It is proved that the collection of blocks of an affine 1-design that yields a linear orthogonal array is a union of parallel classes of hyperplanes in a finite affine space. In particular, for every prime power q and every m ≥ 2 there exists a unique (up to equivalence) complete linear orthogonal array of strength two associated with the classical design of points and hyperplanes in AG(m, q).
متن کامل