Design of Experiments   

Projects

Optimal Blocking Schemes for Fractional Factorial Designs

Systematic sources of variations in factorial experiments can be effectively reduced without biasing the estimates of the treatment effects by grouping the runs into blocks. For full factorial designs optimal blocking schemes are obtained by applying the minimum aberration criterion to the block defining contrast subgroup. A related concept of order of estimability is proposed. For fractional factorial designs, because of the intrinsic difference between treatment factors and block variables, the minimum aberration approach has to be modified. A concept of admissible blocking schemes is proposed for selecting block designs based on multiple criteria. The resulting $2^n$ and $2^{n-p}$ designs are shown to have better overall properties for practical experiments than those in the literature, e.g., the National Bureau of Standards Tables (1957) and Box, Hunter and Hunter (1978).

Paper: Postscript

Interaction Graphs for 3-Level Fractional Factorial Designs

Graph-aided methods for accommodating the estimation of interactions in factorial experiments have become popular among industrial users. Notable among them is the method of linear graphs due to G. Taguchi. Wu and Chen (1992) pointed out some shortcomings of Taguchi's linear graphs and proposed an alternative method. By extending their method we develop some new graphs for 3-level fractional factorial designs. The proposed graphs have two new features: (i) Each edge of the graph can have one or two lines representing the two components of interaction in a 3-level design, (ii) There are two types of vertices and lines. A collection of graphs is given for 27- and 81-run designs.

Paper: Postscript

A Catalogue of Two-Level and Three-Level Fractional Factorial Designs with Small Runs

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.

Paper: (Postscript:   part 1   part 2)

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Other related web pages

• Response Surface Methodology [http://mijuno.larc.nasa.gov/dfc/rsm.html]

• Taguchi Methods [http://mijuno.larc.nasa.gov/dfc/tm.html]

• Conjoint Analysis [http://mijuno.larc.nasa.gov/dfc/ppt/cja.html]