Minimum Aberration 2 k–p Designs
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.
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TL;DR: In this paper, a method to generate fractional factorial split-plot designs with replicated settings of the whole-plot factors is presented, based on the aberration criterion, and a table of designs that are likely to be useful in practice is presented.
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 wholeplot 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.
8 citations
TL;DR: In this paper, the early stages of many real-life experiments involve a large number of factors among which only a few factors are active, and the optimal full-dimensional designs of those earl...
Abstract: The early stages of many real-life experiments involve a large number of factors among which only a few factors are active. Unfortunately, the optimal full-dimensional designs of those earl...
8 citations
TL;DR: A novel “sliced effect hierarchy principle” is introduced and design criteria to generate factorial designs for multi-platform experiments are developed and a theorem is proved that connects the proposed designs to the well-known minimum aberration designs.
Abstract: Multivariate testing is a popular method to improve websites, mobile apps, and email campaigns. A unique aspect of testing in the online space is that it needs to be conducted across multiple platf...
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Cites background from "Minimum Aberration 2 k–p Designs"
...Fries and Hunter (1980) introduced minimum aberration as a natural generalization of maximum resolution....
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...The minimum aberration criterion, suggested by Fries and Hunter (1980), searches for a design with the minimum number of words of length Rmax....
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TL;DR: In this paper, a fractional factorial split-plot (FFSP) design with restricted randomization structure is presented. And the authors discuss the formulation of FFSP designs using integer programming (IP) to achieve various design criteria such as maximum number of clear two-factor interactions and variations on this criterion.
Abstract: Split-plot designs are commonly used in industrial experiments when there are hard-to-change and easy-to-change factors. Due to the number of factors and resource limitations, it is more practical to run a fractional factorial split-plot (FFSP) design. These designs are variations of the fractional factorial (FF) design, with the restricted randomisation structure to account for the whole plots and subplots. We discuss the formulation of FFSP designs using integer programming (IP) to achieve various design criteria. We specifically look at the maximum number of clear two-factor interactions and variations on this criterion.
8 citations
01 Jan 2004
TL;DR: In this article, a collection of three-level fractional factorial designs with 27, 81, 243, and 729 runs is given, extending the work of Chen, Sun and Wu (1993).
Abstract: A common problem experimenters face is the choice of fractional factorial designs. Minimum aberration designs are commonly used in practice. There are situations in which other designs meet practical needs better. A catalogue of designs would help experimenters choose the best design. Based on coding theory, new methods are proposed to efficiently classify and rank fractional factorial designs. A collection of three-level fractional factorial designs with 27, 81, 243 and 729 runs is given. This extends the work of Chen, Sun and Wu (1993), who gave a collection of fractional factorial designs with 16, 27, 32 and 64 runs.
8 citations
Cites background or methods from "Minimum Aberration 2 k–p Designs"
...The minimum aberration criterion (Fries and Hunter, 1980) is to sequentially minimize Aj for j = 1, . . . , n....
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...The minimum aberration criterion (Fries and Hunter, 1980), an extension of the maximum resolution criterion (Box and Hunter, 1961), has been used explicitly or implicitly in the construction of design tables in National Bureau of Standards (1957), Box, Hunter and Hunter (1978, Table 12.15), Wu and…...
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References
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471 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
09 Jun 1976
271 citations
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