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 general and unified approach to the selection of regular fractional factorial designs, which can be applied to experiments that are unblocked, blocked or have a split-plot structure, is proposed.
Abstract: We propose a general and unified approach to the selection of regular fractional factorial designs, which can be applied to experiments that are unblocked, blocked or have a split-plot structure. Our criterion is derived as a good surrogate for the model-robustness criterion of information capacity. In the case of random block effects, it takes the ratio of intra- and interblock variances into account. In most of the cases we have examined, there exist designs that are optimal for all values of that ratio. Examples of optimal designs that depend on the ratio are provided. We also demonstrate that our criterion can further discriminate designs that cannot be distinguished by the existing minimum-aberration criteria.
29 citations
TL;DR: Xu and Cheng as discussed by the authors developed a general complementary design theory for doubling and developed a rule for choosing minimum aberration projection designs from the maximal design with 5N/16 factors.
Abstract: A COMPLEMENTARY DESIGN THEORY FOR DOUBLING By Hongquan Xu 1 and Ching-Shui Cheng 2 University of California, Los Angeles, and University of California, Berkeley August 11, 2006 Chen and Cheng (2006a) discussed the method of doubling for con- structing two-level fractional factorial designs. They showed that for 9N/32 ≤ n ≤ 5N/16, all minimum aberration designs with N runs and n factors are projections of the maximal design with 5N/16 factors which is constructed by repeatedly doubling the 2 5−1 design defined by I = ABCDE. This paper develops a general complementary design the- ory for doubling. For any design obtained by repeated doubling, general identities are established to link the wordlength patterns of each pair of complementary projection designs. A rule is developed for choosing minimum aberration projection designs from the maximal design with 5N/16 factors. It is further shown that for 17N/64 ≤ n ≤ 5N/16, all minimum aberration designs with N runs and n factors are projections of the maximal design with N runs and 5N/16 factors. AMS 2000 subject classifications. Primary 62K15. Key words and phrases. Maximal design, minimum aberration, Pless power moment identity, wordlength pattern. Running title. Doubling and Complementary Designs Supported in part by NSF Grant DMS-0505728 Supported in part by NSF Grant DMS-0505556
28 citations
TL;DR: In this article, a guide is provided for the inclusion of four-level factors into standard two-level factorial designs, where the four level factors can be used to improve the performance of factorials.
Abstract: [This abstract is based on the author's abstract.] A guide is provided for the inclusion of four-level factors into standard two-level factorial designs. Practitioners familiar with two-level fractional factorials often are frustrated when confronted ..
28 citations
Posted Content•
TL;DR: This work provides a combinatorial polynomial time algorithm for arbitrary oracle-presented matroids, that makes repeated use of matroid intersection and an algebraic algorithm for vectorialMatroids.
Abstract: We study the problem of optimizing nonlinear objective functions over matroids presented by oracles or explicitly. Such functions can be interpreted as the balancing of multi-criteria optimization. We provide a combinatorial polynomial time algorithm for arbitrary oracle-presented matroids, that makes repeated use of matroid intersection, and an algebraic algorithm for vectorial matroids.
Our work is partly motivated by applications to minimum-aberration model-fitting in experimental design in statistics, which we discuss and demonstrate in detail.
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TL;DR: The chapter focuses on the identification and determination of the “correct” parameter values of a chemical kinetics model given a set of experimental measurements and on the development of predictive reaction models.
Abstract: Publisher Summary Chemical reaction models are built for several reasons, such as exploratory modeling with the purpose of identifying possible reaction pathways, analyzing one's own experimental data, testing possible experimental trends, or making predictions for the purpose of design and policy assessment. Chemical reaction models are composed from individual reaction steps, either elementary or global. Each reaction step has a prescribed rate law, which is characterized by a set of parameters. The parameter values are collected from the literature, evaluated using theoretical machinery, estimated by empirical rules, or simply guessed. The predictive power of a reaction model is determined by two factors: the authenticity of the reaction steps and the correctness of the rate parameters. The chapter focuses on the identification and determination of the “correct” parameter values of a chemical kinetics model given a set of experimental measurements and on the development of predictive reaction models. The chapter introduces the chemical kinetics with the subject matter and terminology, exposing the specific difficulties and problems associated with optimization of chemical kinetic models and provides guidance to get practical results.
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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