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 Jan 2006
1 citations
Cites background from "Minimum Aberration 2 k–p Designs"
...Menurut Fries & Hunter (1980), tingkat resolusi maksimum yang dapat dicapai untuk 1=p dan 2=p adalah sebagai berikut: • Untuk 1=p maka resolusi maksimum = n • Untuk 2=p maka resolusi maksimum = [2n/3] Dengan n adalah banyaknya faktor yang dicobakan dan [x] adalah nilai bilangan bulat terbesar yang…...
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...Pemilihan struktur rancangan terbaik dilakukan dengan kriteria resolusi maksimum dan minimum-aberration (Fries & Hunter 1980)....
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...Dalam kondisi demikian, Fries & Hunter (1980) memperkenalkan minimum-aberration sebagai kriteria untuk pemilihan rancangan terbaik....
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...Rancangan minimum-aberration (MA) adalah rancangan yang meminimalkan banyaknya kata dalam defin ing relation yang panjangnya minimum (Fries & Hunter 1980)....
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...Minimum aberration Kedua kriteria ters ebut di atas diperlukan untuk mendapatkan struktur rancangan terbaik (Montgomery 2001, Fries & Hunter 1980)....
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TL;DR: In this paper, a partial aliased effect number pattern (P-AENP) was used to assess and select class one two-level compromise designs, and a number of class one clear, strongly clear and general optimal 2 n-m compromise designs with 8, 16, 32 and 64 runs were tabulated.
Abstract: Often, experimenters are only interested in estimating a few factor specified effects. In this paper, we broadly call a design which can reach this target a compromise design. First, for assessing and selecting this kind of designs we introduce a partial aliased effect number pattern (P-AENP), then we use this pattern to study class one two-level compromise designs. Some theoretical results are obtained and a number of class one clear, strongly clear and general optimal $$2^{n-m}$$
compromise designs with 8, 16, 32 and 64 runs are tabulated.
1 citations
TL;DR: In this article, a new class of sliced equidistance designs and a corresponding complementary design theory under the generalized minimum aberration criterion are introduced and two rules are established to search for a generalized minimum-aberration design through its complementary design in a sliced equideistance design.
1 citations
01 Jan 2016
TL;DR: In this paper, the authors show that it is possible to use some subset of all possible runs and still be able to fit a first order polynomial approximation to the response function.
Abstract: In the two-level experiment with k input factors, there are 2 k possible runs. For k = 3, there are only eight runs. But even with five factors, 25 = 32 runs may be prohibitively expensive and time consuming. The question is whether it is possible to use some subset of all possible runs and still be able to fit a first order polynomial approximation to the response function. The answer is yes, but you must give up some resolution in your approximation. The amount of resolution lost is generally in terms of which interaction effects which can be included in your model.
1 citations
01 Jan 2018
TL;DR: This chapter shows that uniformity is intimately connected with many other design criteria and is concerned with randomness, balance between factors and levels of each factor, orthogonality, efficiency, and robustness.
Abstract: Most experimental designs, such as simple random design, random block design, Latin square design, fractional factorial design (FFD, for short), optimal design, and robust design are concerned with randomness, balance between factors and levels of each factor, orthogonality, efficiency, and robustness. From the previous chapters, we see that the uniformity has played an important role in the evaluation and construction of uniform designs. In this chapter, we shall show that uniformity is intimately connected with many other design criteria.
1 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