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 1999
TL;DR: In this article, the authors provide a guide for the inclusion of four-level factors into standard two-level factorial designs, using the same types of experimental design criteria commonly used for designing twolevel fractional factorials.
Abstract: Practitioners, familiar with the design of two-level fractional factorials, are often frustrated when confronted with factors that have more than two levels. This article provides a guide for the inclusion of four-level factors into standard two-level factorial designs. Tables are presented to allow for the design of experiments with two-level and four-level factors using the same types of experimental design criteria commonly used for designing two-level fractional factorials. The concepts of resolution, aberration, and foldover are explained in the context of experiments with two-level and four-level factors. Several new minimum aberration designs that are not in the literature are listed in the tables and new follow-up designs for the recommended experiments are also provided.
5 citations
Cites background from "Minimum Aberration 2 k–p Designs"
...Aberration, introduced by Fries and Hunter (1980), is a concept that is similar to, but more discriminating than resolution....
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TL;DR: In this article, the authors proposed repair resolution central composite (RRCC) designs, which repaired the portion containing factorial fractions of resolution III or IV and de-aliased the words of length four or lower.
Abstract: Standard central composite design (CCD) originally requires that its factorial portion contains a full factorial design or fractional factorial design of resolution V or higher so that all effects of vital interest could be estimated. A CCD can be an ideal choice for lower number of factors (k). For k > 5, the standard CCD becomes very large and when, with the purpose of reduction of design size, the initial fractional factorial of resolution III or IV is used, the lower order effects are confounded. Block and Mee (2001) proposed some economical designs for k > 5. The designs were named as repaired resolution central composite (RRCC) designs; these actually repaired the portion containing factorial fractions of resolution III or IV. After repairing, the words of length four or lower were de-aliased and the effects of vital importance became estimable. In this study, some new versions of RRCC designs are constructed. All classes of designs are studied for their robustness to missing data. Loss of missing d...
5 citations
TL;DR: In this article, the authors present a methodology for constructing two-level split-plot and multistage experiments based on the Kronecker product representation of orthogonal designs and can be used for any number of stages.
Abstract: Most of today’s complex systems and processes involve several stages through which input or the raw material has to go before the final product is obtained. Also in many cases factors at different stages interact. Therefore, a holistic approach for experimentation that considers all stages at the same time will be more efficient. However, there have been only a few attempts in the literature to provide an adequate and easy-to-use approach for this problem. In this paper, we present a novel methodology for constructing two-level split-plot and multistage experiments. The methodology is based on the Kronecker product representation of orthogonal designs and can be used for any number of stages, for various numbers of subplots and for different number of subplots for each stage. The procedure is demonstrated on both regular and nonregular designs and provides the maximum number of factors that can be accommodated in each stage. Furthermore, split-plot designs for multistage experiments with good proj...
5 citations
TL;DR: In this article, the authors propose a new criterion that is defined on a column of the design matrix to measure the aliasing of the effect assigned to this column and effects involving other factors.
5 citations
01 Jan 2007
TL;DR: In this paper, the ADX Interface for design of experiments in SAS/QC® makes it very easy to design and analyze the most common fractional factorial experiments of this type.
Abstract: A complex manufacturing process has many stages, with different factors active at different stages. How do you discover which factors are important at a particular stage, and what factor, or factors, from an early stage interacts with one, or more, at a later stage (e.g. the source of raw material versus final packaging)? Split-plot experiments come to the rescue! They are a key tool for improving final product quality by studying how all stages affect final product quality. Until recently the design of fractional factorial experiments with more than one stage was not trivial. In this paper we show how the ADX Interface for design of experiments in SAS/QC® makes it very easy to design and analyze the most common experiments of this type. For more complex situations, recent advances in PROC FACTEX enable you to custom design experiments for processes with several stages. Two examples are presented showcasing these new features in ADX and PROC FACTEX.
5 citations
Additional excerpts
...Huang et al (1998), and Bingham and Sitter (1999, 2001) have applied the concept of minimum aberration (Fries and Hunter (1980)) to splitplot designs, giving comprehensive tables for small to moderately sized minimum aberration split-plot designs, while Kulahci et al (2006) have discussed…...
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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