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Journal ArticleDOI

Minimum Aberration 2 k–p Designs

01 Nov 1980-Technometrics (Taylor & Francis Group)-Vol. 22, Iss: 4, pp 601-608
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.
Citations
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Journal ArticleDOI
TL;DR: In this paper, a method to generate fractional factorial split-plot designs with replicated settings of the whole-plot factors is presented. Butler et al. use a cheese-making experiment to demonstrate the practical relevance of designs with replicas of these factors.
Abstract: When it is impractical to perform the experimental runs of a fractional factorial design in a completely random order, restrictions on the randomization can be imposed. The resulting design is said to have a split-plot, or nested, error structure. Similarly to fractional factorials, fractional factorial split-plot designs can be ranked by using the aberration criterion. Techniques that generate the required designs systematically presuppose unreplicated settings of the whole-plot factors. We use a cheese-making experiment to demonstrate the practical relevance of designs with replicated settings of these factors. We create such designs by splitting the whole plots according to one or more subplot effects. We develop a systematic method to generate the required designs and we use the method to create a table of designs that is likely to be useful in practice.

67 citations

Journal ArticleDOI
TL;DR: In this paper, the goodness of multi-level supersaturated designs can be judged by the generalized minimum aberration criterion proposed by Xu and Wu (2001) and general methods for constructing optimal multilevel supersaturated design are proposed.
Abstract: Author(s): Xu, Hongquan; Wu, CFJ | Abstract: A supersaturated design is a design whose run size is not large enough for estimating all the main effects. The goodness of multi-level supersaturated designs can be judged by the generalized minimum aberration criterion proposed by Xu and Wu (2001). Optimal supersaturated designs are shown to have a periodic property and general methods for constructing optimal multilevel supersaturated designs are proposed. Inspired by the Addelman-Kempthorne construction of orthogonal arrays, optimal multi-level supersaturated designs are given in an explicit form: columns are labeled with linear or quadratic polynomials and rows are points over a finite field. Additive characters are used to study the properties of resulting designs. Some small optimal supersaturated designs of 3, 4 and 5 levels are listed with their properties.

65 citations

Journal ArticleDOI
TL;DR: A set of optimality criteria is proposed to assess the performance of designs for factor screening, projection, and interaction detection, and a three-step approach to search for optimal designs is proposed.
Abstract: Orthogonal arrays (OAs) are widely used in industrial experiments for factor screening. Suppose that only a few of the factors in the experiments turn out to be important. An OA can be used not only for screening factors, but also for detecting interactions among a subset of active factors. In this article a set of optimality criteria is proposed to assess the performance of designs for factor screening, projection, and interaction detection, and a three-step approach is proposed to search for optimal designs. Combinatorial and algorithmic construction methods are proposed for generating new designs. Permutations of levels are used for improving the eligibility and estimation efficiency of the projected designs. The techniques are then applied to search for best three-level designs with 18 and 27 runs. Many new, efficient, and practically useful nonregular designs are found and their properties are discussed.

65 citations

01 Jan 2001
TL;DR: In this paper, it was shown that two designs are equivalent if the Hamming distances between the points are the same in all possible dimensions, where p is the number of factors.
Abstract: Two designs for a fractional factorial experiment are equivalent if one can be obtained from the other by reordering the treatment combinations, relabeling the factors and relabeling the factor levels. Designs can be viewed as sets of points in p- dimensional space, where p is the number of factors. It is shown that, in this setting, two designs are equivalent if the Hamming distances between the points are the same in all possible dimensions. An algorithm is given, based on this representation, that can detect distinct designs for 2 p experiments without a complete search of all reorderings and relabelings in the fraction. In addition, if two designs are equivalent, the algorithm gives a set of permutations which map one design to the other.

65 citations


Cites background from "Minimum Aberration 2 k–p Designs"

  • ...The wordlength pattern also uniquely determines the design for 2p−3 and 2p−4 group-generated minimum aberration (Fries and Hunter (1980)) fractions....

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Journal ArticleDOI
TL;DR: Based on the effect hierarchy principle in experimental design, an aliased effect-number pattern (AENP, or AP for short) is proposed to judge two-level regu- lar designs; it contains the basic information of all effects aliased with other effects at varying severity degrees in a design.

64 citations

References
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Book
01 Jan 1978

5,151 citations

Book
23 Jun 1976
TL;DR: In conclusion, the size of Industrial Experiments, Fractional Replication--Elementary, and Incomplete Factorials are found to be about the same as that of conventional comparison experiments.
Abstract: Introduction. Simple Comparison Experiments. Two Factors, Each at Two Levels. Two Factors, Each at Three Levels. Unreplicated Three--Factor, Two--Level Experiments. Unreplicated Four--Factor, Two--Level Experiments. Three Five--Factor, Two--Level Unreplicated Experiments. Larger Two--Way Layouts. The Size of Industrial Experiments. Blocking Factorial Experiments, Fractional Replication--Elementary. Fractional Replication--Intermediate. Incomplete Factorials. Sequences of Fractional Replicates. Trend--Robust Plans. Nested Designs. Conclusions and Apologies.

311 citations

Journal ArticleDOI
TL;DR: Incomplete Factorials, Fractional Replication, Intermediate Factorial, and Nested Designs as discussed by the authors are some of the examples of incomplete Factorial Experiments and incomplete fractional replicates.
Abstract: Introduction. Simple Comparison Experiments. Two Factors, Each at Two Levels. Two Factors, Each at Three Levels. Unreplicated Three--Factor, Two--Level Experiments. Unreplicated Four--Factor, Two--Level Experiments. Three Five--Factor, Two--Level Unreplicated Experiments. Larger Two--Way Layouts. The Size of Industrial Experiments. Blocking Factorial Experiments, Fractional Replication--Elementary. Fractional Replication--Intermediate. Incomplete Factorials. Sequences of Fractional Replicates. Trend--Robust Plans. Nested Designs. Conclusions and Apologies.

252 citations