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.
Citations
More filters
TL;DR: In this paper, a new criterion is proposed for supersaturated designs with quantitative factors, in which level permutation within one or more factors could result in different geometrical structures.
3 citations
31 Jan 2021
TL;DR: In this article, the problem of selecting two-level designs under the baseline parameterization when some two-factor interactions are important is considered, and a minimum aberration criterion is proposed.
Abstract: This article considers the problem of selecting two-level designs under the baseline parameterisation when some two-factor interactions are important. We propose a minimum aberration criterion, whi...
3 citations
Cites background from "Minimum Aberration 2 k–p Designs"
...Firstly proposed by Fries and Hunter (1980), the minimum aberration is a popular criterion for selecting two-level fractional factorial designs....
[...]
Posted Content•
TL;DR: In this paper, the authors present some optimal criteria to evaluate model robustness of non-regular two-level fractional factorial designs based on minimizing the sum of squares of all the off-diagonal elements in the information matrix.
Abstract: We present some optimal criteria to evaluate model-robustness of non-regular two-level fractional factorial designs. Our method is based on minimizing the sum of squares of all the off-diagonal elements in the information matrix, and considering expectation under appropriate distribution functions for unknown contamination of the interaction effects. By considering uniform distributions on symmetric support, our criteria can be expressed as linear combinations of $B_s(d)$ characteristic, which is used to characterize the generalized minimum aberration. We give some empirical studies for 12-run non-regular designs to evaluate our method.
3 citations
TL;DR: Application to small run sizes shows that the use of efficient computational algorithms to construct generalized minimum aberration designs perform almost as well as complete search, but with much less computing time, which strongly suggests that these algorithms should be successful in finding good designs for larger run sizes.
Abstract: SYNOPTIC ABSTRACTGeneralized minimum aberration was introduced by Deng and Tang (1999) as a criterion for comparing and assessing the “goodness” of nonregular fractional factorial designs. For small run sizes, generalized minimum aberration designs can be obtained by a complete search of Hadamard matrices; however, for larger run sizes a complete search is impractical. The main purpose of this paper is to study the use of efficient computational algorithms to construct generalized minimum aberration designs. Application to small run sizes shows that our algorithms perform almost as well as complete search, but with much less computing time. This strongly suggests that our algorithms should be successful in finding good designs for larger run sizes.
3 citations
Dissertation•
01 Jan 2011
TL;DR: In this paper, a decision theory approach is explored to improve the guidance available to experimenters in choosing a good design and analysing data, which is particularly important when there is commercial pressure to minimise the size of the experiment.
Abstract: Unreplicated two level fractional factorial designs are a common type of experimental design used in the early stages of industrial experimentation. They allow considerable information about the effects of several factors on the response to be obtained with a relatively small number of runs. The aim of this thesis is to improve the guidance available to experimenters in choosing a good design and analysing data. This is particularly important when there is commercial pressure to minimise the size of the experiment. A design is usually chosen based on optimality, either in terms of a variance criterion or estimability criteria such as resolution. This is given the number of factors, number of levels of each factor and number of runs available. A decision theory approach is explored, which allows a more informed choice of design to be made. Prior distributions on the sizes of effects are taken into consideration, and then a design chosen from a candidate set of designs using a utility function relevant to the objectives of the experiment. Comparisons of the decision theoretic methods with simple rules of thumb are made to determine when the more complex approach is necessary. Fully Bayesian methods are rarely used in multifactor experiments. However there is virtually always some prior knowledge about the sizes of effects and so using this in a Bayesian data analysis seems natural. Vague and more informative priors are
3 citations
References
More filters
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