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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Dissertation•
01 Dec 2011
TL;DR: In this article, a simple method for generating its pattern is proposed, which can be linked to the three main criteria for measuring the degree of aliasing in a manner devoid of mathematical complications.
Abstract: Design of Experiments (DOE) is a powerful technique for understanding, characterising and modelling products and processes and improving their performance. Whilst the bulk of its literature revolves around how it should be applied, little attention, if any, is devoted to the manner in which it is being implemented in practice particularly in manufacturing. One objective of this study was to bridge this gap by reviewing practical applications in three manufacturing journals. This revealed not only limited use but also multiple deficiencies. Many of these concerned a lack of familiarity with the concept of aliasing; the use of fractional factorial designs and pooling methods to analyse unreplicated trials; and a misunderstanding of the concepts underpinning the use and interpretation of p-values and factorial effects’ importance measures. With respect to aliasing, a novel simple method for generating its pattern is proposed. Besides its ease of application, it can be linked to the three main criteria for measuring the degree of aliasing (maximum resolution, minimum aberration and generalised minimum aberration) in a manner devoid of mathematical complications. Regarding the use of fractional factorial designs and pooling methods, simulation experiments were used to assess the performance of certain experimentation strategies to arrive at the same conclusions had a full factorial trial been performed. In the context of two-level designs, the L\(_{16}\) together with the Pooling Up method or the Half Normal Probability plot yielded a satisfactory performance. Similarly, the strategy of using the Best Subset selection procedure in conjunction with the L\(_{18}\) design was the best among the examined three-level ones. To attain a robust performance, it was found that the use of small designs such as the L\(_8\) and the L\(_9\) should, as far as possible, be avoided. The concepts concerning the use of the p-values and the effect’s importance measures are clarified and to facilitate communication between Engineers, Managers and Statisticians, an importance measure that can be related to three quality engineering techniques is suggested.
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TL;DR: In this article, a method of tripling for three-level design, which triples both the run size and number of factors of the initial design, is proposed by orthogonally combining all possible level permutations of its initial design.
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TL;DR: In this paper, the minimum breakdown criterion is proposed to quantify the robustness of designs in blocks of size two and a new class of robust designs, called minimum breakdown designs, is defined.
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TL;DR: A new minimum aberration-type criterion for designing experiments with two- and four-level factors is proposed, motivated by a Bayesian framework, which helps in overcoming the ad hoc nature of effect ordering in the existing minimum aberrations-type criteria.
Abstract: SUMMARY Motivated by a Bayesian framework, we propose a new minimum aberration-type criterion for designing experiments with two- and four-level factors. The Bayesian approach helps in overcoming the ad hoc nature of effect ordering in the existing minimum aberration-type criteria. The approach is also capable of distinguishing between qualitative and quantitative factors. Numerous examples are given to demonstrate its advantages.
10 citations
TL;DR: In this article, the construction of optimal two-level block designs with respect to the B1-GMC criterion is considered. And some optimal block designs are obtained by utilizing doubling theory and MaxC2 design.
Abstract: In practice, to reduce systematic variation and increase precision of effect estimation, a practical design strategy is then to partition the experimental units into homogeneous groups, known as blocks. It is an important issue to study the optimal way on blocking the experimental units. Blocked general minimum lower order confounding (B1-GMC) is a new criterion for selecting optimal block designs. The paper considers the construction of optimal two-level block designs with respect to the B1-GMC criterion. By utilizing doubling theory and MaxC2 design, some optimal block designs with respect to the B1-GMC criterion are obtained.
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Cites background from "Minimum Aberration 2 k–p Designs"
...The criteria include maximum resolution (Box and Hunter, 1961), minimum aberration (Fries and Hunter, 1980), clear effects (Wu and Chen, 1992) and maximum estimation capacity (Sun, 1993)....
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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