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: The alias length pattern (ALP) was proposed to characterize the aliasing among two-factor interactions for regular two-level fractional factorial designs of resolution I I I and I V as mentioned in this paper.
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TL;DR: In this paper, the effects of m two-level factors using n = 2m−k experimental units arranged in 2p blocks of size 2m −k−p were investigated.
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TL;DR: In this article, the authors present a more concise representation of the popular experimental design generators for fractional factorial designs, indexed by the information that the experimenter will start with: the number of factors and the desired resolution for the experiment.
Abstract: This modest paper contains a much more concise representation of the popular experimental design generators for fractional factorial designs. The information is indexed by the information that the experimenter will start with: the number of factors and the desired resolution for the experiment. Its format facilitates the exploration of the effect of changing the experimental design by using a different number of factors or by changing the experiment resolution.
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TL;DR: In this article, the authors prove several important properties of 2 −k-p minimum aberration (MA) designs with k > 2, where n = 2−k −p is the number of runs.
Abstract: In this article we prove several important properties of 2^{k-p} minimum aberration (MA) designs with k>2, where n=2^{k-p} is the number of runs. We develop a simple method to build MA designs of resolution III. Furthermore, we introduce a simple relationship, based on product of polynomials, for computing their word-length patterns.
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TL;DR: In this article, the authors define a criterion to check whether a given fraction is saturated or not, and compute the number of saturated fractions, which can be used as actual methods to build saturated fractions.
Abstract: In this paper we study saturated fractions of a two-factor design under the simple effect model In particular, we define a criterion to check whether a given fraction is saturated or not, and we compute the number of saturated fractions All proofs are constructive and can be used as actual methods to build saturated fractions Moreover, we show how the theory of Markov bases for contingency tables can be applied to two-factor designs for moving between the designs with given margins
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471 citations
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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