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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01 Mar 2005
4 citations
29 Jan 2007
TL;DR: In this article, a sequential algorithm is developed for constructing efficient fractional factorial designs, which only allows a design to be constructed from its minimum aberration pro jection in the sequential build-up process.
Abstract: 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 pro jection in the sequential build-up process To efficiently identify nonisomorphic designs, designs are divided into different categories according to their moment pro jection patterns A fast isomorphism check procedure is developed by matching the factors using their delete-one-factor pro jections 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 128-run designs of resolution 4 up to 30 factors, all 256-run designs of resolution 4 up to 17 factors, all 512-run designs of resolution 5, all 1024-run designs of resolution 6, and all 2048- and 4096-run designs of resolution 7
4 citations
13 Feb 2007
TL;DR: This paper explains some basics of fractional factorial split plot designs and shows how to use the concept of partial design resolution to produce better designs based on specific test objectives.
Abstract: The c haracteristics and objectives of development tests in distribut ed live, virtual, and constructive joint environments favor fractional factorial split -plot experimental designs . Development tes ts conducted in joint environments are key components of the Department of Defense transformational planning initiative to test as we fight . Joint operations have become the mainstay of war fighting. But t he only practical way to assemble joint environment s for testing is to link various live entities , virtual operator - or hardware -in -the loop simulations , and constructive simulat ion s ( simulated people operating simulated systems )-- all located at many geographically -dispersed test facilities . Such distributed tests are expensive and difficult to execute, resulting in many practical limitations that restrict the ability to completel y randomize trials. Objective s of development tests in joint environments include evaluating design alternative s based on joint mission effectiveness and assessing the robustness of design alternatives to uncontrollable sources of variation . These objecti ves and restrictions lead to fractional factorial designs with split plot components. This paper explains some basics of fractional factorial split plot designs and shows how to use the concept of partial design resolution to produce better designs based o n specific test objectives. An example using air -launched data link weapon s is used to illustrate design considerations and analysis concepts.
4 citations
TL;DR: In this paper, a complete catalogue of optimal blocked regular mixed factorial designs of the above two types with 16 or 32 runs is given, together with an appropriate ordering of the number of alias or confounding relations.
4 citations
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