A catalogue of two-level and three-level fractional factorial designs with small runs
TL;DR: In this paper, the algebraic structure of fractional factorial (FF) designs with minimum aberration is explored and an algorithm for constructing complete sets of FF designs is proposed.
Abstract: Summary Fractional factorial (FF) designs with minimum aberration are often regarded as the best designs and are commonly used in practice. There are, however, situations in which other designs can meet practical needs better. A catalogue of designs would make it easy to search for 'best' designs according to various criteria. By exploring the algebraic structure of the FF designs, we propose an algorithm for constructing complete sets of FF designs. A collection of FF designs with 16, 27, 32 and 64 runs is given.
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TL;DR: In this paper, a generalized minimum aberration criterion for comparing asymmetrical fractional factorial designs is proposed, which is independent of the choice of treatment contrasts and thus model-free.
Abstract: By studying treatment contrasts and ANOVA models, we propose a generalized minimum aberration criterion for comparing asymmetrical fractional factorial designs. The criterion is independent of the choice of treatment contrasts and thus model-free. It works for symmetrical and asymmetrical designs, regular and nonregular designs. In particular, it reduces to the minimum aberration criterion for regular designs and the minimum G 2 -aberration criterion for two-level nonregular designs. In addition, by exploring the connection between factorial design theory and coding theory, we develop a complementary design theory for general symmetrical designs, which covers many existing results as special cases.
309 citations
TL;DR: In this paper, the authors introduce an algorithm that constructs the set of all non-isomorphic two-level fractional factorial split-plot designs more efficiently than existing methods.
Abstract: It is often impractical to perform the experimental runs of a fractional factorial in a completely random order, In these cases, restrictions on the randomization of the experimental trials are imposed and the design is said to have a split-plot structure. We rank these fractional factorial split-plot designs similarly to fractional factorials using the aberration criterion to find the minimum-aberration design. We introduce an algorithm that constructs the set of all nonisomorphic two-level fractional factorial split-plot designs more efficiently than existing methods. The algorithm can be easily modified to efficiently produce sets of all nonisomorphic fractional factorial designs, fractional factorial designs in which the number of levels is a power of a prime, and fractional factorial split-plot designs in which the number of levels is a power of a prime.
154 citations
01 Jan 2001
TL;DR: In this paper, a new combinatorial criterion, called minimum moment aberration, is proposed for assessing the goodness of nonregular designs and supersaturated designs, which is a good surrogate with tremendous computational advantages for many statistically justified criteria, such as minimum G2-aberrration, generalized minimum aberration and E(s2).
Abstract: Nonregular designs are used widely in experiments due to their run size economy and flexibility. These designs include the Plackett-Burman designs and many other symmetrical and asymmetrical orthogonal arrays. Supersaturated designs have become increasingly popular in recent years because of the potential in saving run size and its technical novelty. In this paper, a novel combinatorial criterion, called minimum moment aberration, is proposed for assessing the goodness of nonregular designs and supersaturated designs. The new criterion, which is to sequentially minimize the power moments of the number of coincidence among runs, is a good surrogate with tremendous computational advantages for many statistically justified criteria, such as minimum G2-aberrration, generalized minimum aberration and E(s2). In addition, the minimum moment aberration is conceptually simple and convenient for theoretical development. The general theory developed here not only unifies several separate results, but also provides many novel results on nonregular designs and supersaturated designs.
152 citations
Cites background from "A catalogue of two-level and three-..."
...The special case of Corollary 8 for two-level supersaturated designs and E(s2) optimality is first obtained by Tang and Wu (1997) (for the first statement) and Cheng (1997)....
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TL;DR: In this article, the performance of minimum aberration two-level fractional factorial designs is studied under two criteria of model robustness, i.e., the number of aliases of main effects and the sum of squares of the sizes of alias sets of two-factor interactions.
Abstract: Summary. The performance of minimum aberration two-level fractional factorial designs is studied under two criteria of model robustness. Simple sufficient conditions for a design to dominate another design with respect to each of these two criteria are derived. It is also shown that a minimum aberration design of resolution IlIl or higher maximizes the number of two-factor interactions which are not aliases of main effects and, subject to that condition, minimizes the sum of squares of the sizes of alias sets of two-factor interactions. This roughly says that minimum aberration designs tend to make the sizes of the alias sets very uniform. It follows that minimum aberration is a good surrogate for the two criteria of model robustness that are studied here. Examples are given to show that minimum aberration designs are indeed highly efficient.
139 citations
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...(Fries and Hunter (1980), p....
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TL;DR: It is shown how the split-plot structure affects estimation, precision, and the use of resources in fractional factorial design and how these issues affect design selection in a real industrial experiment.
Abstract: It is often impractical to perform experimental runs of a fractional factorial in a completely random order. In these cases, restrictions are imposed on the randomization of the experimental trials, and the design is said to have a split-plot structure...
131 citations
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TL;DR: The 2 k-p Fractional Factorial Designs Part I. as discussed by the authors is a collection of fractional fractional factorial designs with a focus on the construction of the construction.
Abstract: (2000). The 2 k—p Fractional Factorial Designs Part I. Technometrics: Vol. 42, No. 1, pp. 28-47.
449 citations
TL;DR: In this article, the concept of aberration is proposed as a way of selecting the best designs from those with maximum resolution, and algorithms are presented for constructing these minimum aberration designs.
Abstract: For studying k variables in N runs, all 2 k–p designs of maximum resolution are not equally good. In this paper the concept of aberration is proposed as a way of selecting the best designs from those with maximum resolution. Algorithms are presented for constructing these minimum aberration designs.
420 citations