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Moment aberration projection for nonregular fractional factorial designs
 Technometrics
, 2005
"... Nonregular fractional factorial designs, such as Plackett–Burman designs, are widely used in industrial experiments for run size economy and flexibility. A novel criterion, called moment aberration projection, is proposed to rank and classify nonregular designs. It measures the goodness of a design ..."
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Cited by 9 (6 self)
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Nonregular fractional factorial designs, such as Plackett–Burman designs, are widely used in industrial experiments for run size economy and flexibility. A novel criterion, called moment aberration projection, is proposed to rank and classify nonregular designs. It measures the goodness of a design through moments of the number of coincidences between the rows of its projection designs. The new criterion is used to rank and classify designs of 16, 20, and 27 runs. Examples are given to illustrate that the ranking of designs is supported by other design criteria. KEY WORDS:
Algorithmic Construction of Efficient Fractional Factorial Designs With Large Run Sizes
, 2007
"... Fractional factorial designs are widely used in practice and typically chosen according to the minimum aberration criterion. A sequential algorithm is developed for constructing efficient fractional factorial designs. A construction procedure is proposed that only allows a design to be constructed f ..."
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Cited by 9 (3 self)
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Fractional factorial designs are widely used in practice and typically chosen according to the minimum aberration criterion. A sequential algorithm is developed for constructing efficient fractional factorial designs. A construction procedure is proposed that only allows a design to be constructed from its minimum aberration projection in the sequential buildup process. To efficiently identify nonisomorphic designs, designs are divided into different categories according to their moment projection patterns. A fast isomorphism check procedure is developed by matching the factors using their deleteonefactor projections. A method is proposed for constructing minimum aberration designs using only a partial catalog of some good designs. Minimum aberration designs are constructed for 128 runs up to 64 factors, 256 runs up to 28 factors, and 512, 1024, 2048, and 4096 runs up to 23 or 24 factors. Furthermore, this algorithm is used to completely enumerate all 128run designs of resolution 4 up to 30 factors, all 256run designs of resolution 4 up to 17 factors, all 512run designs of resolution 5, all 1024run designs of resolution 6, and all 2048 and 4096run designs of resolution 7.
Uniformity In Fractional Factorials
 IN MONTE CARLO AND QUASIMONTE CARLO METHODS 2000
, 1999
"... The issue of uniformity is crucial in quasiMonte Carlo methods and in the design of computer experiments. In this paper we study the role of uniformity in fractional factorial designs. For fractions of two or threelevel factorials, we derive results connecting orthogonality, aberration and unifor ..."
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Cited by 2 (1 self)
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The issue of uniformity is crucial in quasiMonte Carlo methods and in the design of computer experiments. In this paper we study the role of uniformity in fractional factorial designs. For fractions of two or threelevel factorials, we derive results connecting orthogonality, aberration and uniformity and show that these criteria agree quite well. This provides further justification for the criteria of orthogonality or minimum aberration in terms of uniformity. Our results refer to several natural measures of uniformity and we consider both regular and nonregular fractions. The theory developed here has the potential of significantly reducing the complexity of computation for searching minimum aberration designs.
A SENSITIVE ALGORITHM FOR DETECTING THE INEQUIVALENCE OF HADAMARD MATRICES
"... Abstract. A Hadamard matrix of side n is an n × n matrix with every entry either 1 or −1, which satisfies HH T = nI. Two Hadamard matrices are called equivalent if one can be obtained from the other by some sequence of row and column permutations and negations. To identify the equivalence of two Had ..."
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Cited by 1 (0 self)
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Abstract. A Hadamard matrix of side n is an n × n matrix with every entry either 1 or −1, which satisfies HH T = nI. Two Hadamard matrices are called equivalent if one can be obtained from the other by some sequence of row and column permutations and negations. To identify the equivalence of two Hadamard matrices by a complete search is known to be an NP hard problem when n increases. In this paper, a new algorithm for detecting inequivalence of two Hadamard matrices is proposed, which is more sensitive than those known in the literature and which has a close relation with several measures of uniformity. As an application, we apply the new algorithm to verify the inequivalence of the known 60 inequivalent Hadamard matrices of order 24; furthermore, we show that there are at least 382 pairwise inequivalent Hadamard matrices of order 36. The latter is a new discovery. 1.
Statistical Isomorphism of ThreeLevel Fractional Factorial Designs
"... From a statistician's standpoint, the interesting kind of isomorphism for fractional factorial designs depends on the statistical application. Combinatorially isomorphic fractional factorial designs may have dierent statistical properties when factors are quantitative. This idea is illustrated ..."
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From a statistician's standpoint, the interesting kind of isomorphism for fractional factorial designs depends on the statistical application. Combinatorially isomorphic fractional factorial designs may have dierent statistical properties when factors are quantitative. This idea is illustrated by using Latin squares of order 3 to obtain fractions of the 33 factorial design in 18 runs. Key words: eciency; optimal design; orthogonal array. 1
Journal of Statistical Planning and Inference
"... This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal noncommercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or sel ..."
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This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal noncommercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier’s archiving and manuscript policies are encouraged to visit: