Maximizing data information requires careful selection, termed design, of the points at which data are observed. Experimental design is reviewed here for broad classes of data collection and analysis problems, including: fractioning techniques based on orthogonal arrays, Latin hypercube designs and their variants for computer experimentation, efficient design for data mining and machine learning applications, and sequential design for active learning. © 2012 Wiley Periodicals, Inc. © 2012 Wiley Periodicals, Inc.

Experimental design

It is more than a decade since Genichi Taguchi's ideas on quality improvement were inrroduced in the United States. His parameter-design approach for reducing variation in products and processes has generated a great deal of interest among both quality practitioners and statisticians. The statistical techniques used by Taguchi to implement parameter design have been the subject of much debate, however, and there has been considerable research aimed at integrating the parameter-design principles with well-established statistical techniques. On the other hand, Taguchi and his colleagues feel that these research efforts by statisticians are misguided and reflect a lack of understanding of the engineering principles underlying Taguchi's methodology. This panel discussion provides a forum for a technical discussion of these diverse views. A group of practitioners and researchers discuss the role of parameter design and Taguchi's methodology for implementing it. The topics covered include the importance of vari...

Taguchi's parameter design: a panel discussion

By studying treatment contrasts and ANOVA models, we propose a generalized minimum aberration criterion for comparing asymmetrical fractional factorial designs. The criterion is independent of the choice of treatment contrasts and thus model-free. It works for symmetrical and asymmetrical designs, regular and nonregular designs. In particular, it reduces to the minimum aberration criterion for regular designs and the minimum G 2 -aberration criterion for two-level nonregular designs. In addition, by exploring the connection between factorial design theory and coding theory, we develop a complementary design theory for general symmetrical designs, which covers many existing results as special cases.

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Generalized minimum aberration for asymmetrical fractional factorial designs

We review major developments in the design of experiments, offer our thoughts on important directions for the future, and make specific recommendations for experimenters and statisticians who are students and teachers of experimental design, practitioners of experimental design, and researchers jointly exploring new frontiers. Specific topics covered are optimal design, computer-aided design, robust design, response surface design, mixture design, factorial design, block design, and designs for nonlinear models.

Experimental Design: Review and Comment

Summary Fractional factorial (FF) designs with minimum aberration are often regarded as the best designs and are commonly used in practice. There are, however, situations in which other designs can meet practical needs better. A catalogue of designs would make it easy to search for 'best' designs according to various criteria. By exploring the algebraic structure of the FF designs, we propose an algorithm for constructing complete sets of FF designs. A collection of FF designs with 16, 27, 32 and 64 runs is given.

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A catalogue of two-level and three-level fractional factorial designs with small runs

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.

Minimum Aberration 2 k–p Designs

Fractional factorial designs-especially the twolevel designs-are useful in a variety of experimental situations, for example, (i) screening studies in which only a subset of the variables is expected to be important, (ii) research investigations in which certain interactions are expected to be negligible and (iii) experimental programs in which groups of runs are to be performed sequentially, ambiguities being resolved as the investigation evolves (see Box, Hunter and Hunter, 1978). The literature on fractional factorial designs is extensive. For references before 1969, see the comprehensive bibliography of Herzberg and Cox (1969). For more recent references, see Daniel (1976) and Joiner (1975-79). A useful concept associated with 2k-P fractional factorial designs is that of resolution (Box and Hunter, 1961). A design is of resolution R if no cfactor effect is confounded with any other effect containing less than R c factors. For example, a design of resolution III does not confound main effects with one another but does confound main effects with two-factor interactions, and a design of resolution IV does not confound main effects with two-factor interactions but does confound two-factor interactions with one another. The resolution of a two-level fractional factorial design is the length of the shortest word in the defining relation. Usually an experimenter will prefer to use a design which has the highest

Arthur Fries

Papers

Minimum Aberration 2 k–p Designs

Minimum Aberration 2k-p Designs