Classification of two-level factorial fractions

“…An indicator polynomial function is associated with a fraction with no replications. This approach was developed in Fontana et al (1996), Fontana et al (2000), Ye (2003) for 2-level design and generalized in Ye (2004), Pistone and Rogantin (2006).…”

Section: Introductionmentioning

confidence: 99%

Hilbert Bases for Orthogonal Arrays

Carlini

Pistone

2007

Journal of Statistical Theory and Practice

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Abstract. In this paper, we relate the problem of generating all 2-level orthogonal arrays of given dimension and force, i.e. elements in OA(n, m), where n is the number of factors and m the force, to the solution of an Integer Programming problem involving rational convex cones. We do not restrict the number of points in the array, i.e. we admit any number of replications. This problem can be theoretically solved by means of Hilbert bases which form a finite generating set for all the elements in in the infinite set OA(n, m). We discuss some examples which are explicitly solved with a software performing Hilbert bases computation.

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“…The interested reader can find further information, including the proofs of the propositions in Fontana (2013) itself and in Fontana et al (2000), Pistone and Rogantin (2008), Fontana and Pistone (2010a) and Fontana and Pistone (2010b).…”

Section: Algebraic Generation Of Oasmentioning

confidence: 99%

“…This theory puts neither a restriction on the number of levels of each factor nor on the orthogonality constraints. It also makes use of commutative algebra (see Pistone and Wynn 1996), and generalizes the approach to two-level designs as discussed in Fontana, Pistone, and Rogantin (2000). The definition of strata provided in Section 2 makes it possible to transform each OFFD into a solution of a homogeneous system of linear equations where the unknowns are positive integers.…”

Section: Introductionmentioning

confidence: 99%

Minimum-Size Mixed-Level Orthogonal Fractional Factorial Designs Generation: ASAS-Based Algorithm

Fontana¹,

Sampò²

2013

J. Stat. Soft.

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Orthogonal fractional factorial designs (OFFDs) are frequently used in many fields of application, including medicine, engineering and agriculture. In this paper we present a software tool for the generation of minimum size OFFDs. The software, that has been implemented in SAS/IML, puts neither a restriction on the number of levels of each factor nor on the orthogonality constraints. The algorithm is based on the joint use of polynomial counting function and complex coding of levels and follows the approach presented in Fontana (2013).

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Classification of two-level factorial fractions

Cited by 82 publications

References 16 publications

Indicator function and complex coding for mixed fractional factorial designs

Indicator function and complex coding for mixed fractional factorial designs

Hilbert Bases for Orthogonal Arrays

Minimum-Size Mixed-Level Orthogonal Fractional Factorial Designs Generation: ASAS-Based Algorithm

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