Research Seminars

Optimal design: getting more out of experiments with hard-to-change factors

We introduce a new method for generating optimal split-plot designs. These designs are optimal in the sense that they are efficient for estimating the fixed effects of the statistical model that is appropriate given the split-plot design structure. One advantage of the method is that it does not require the prior specification of a candidate set. This makes the production of split-plot designs computationally feasible in situations where the candidate set is too large to be tractable. The method allows for flexible choice of the sample size and supports inclusion of both continuous and categorical factors. The model can be any linear regression model and may include arbitrary polynomial terms in the continuous factors and interaction terms of any order. We demonstrate the usefulness of this flexibility with a 100-run polypropylene experiment involving 11 factors where we found a design that is substantially more efficient than designs that are produced by using other approaches.

Optimal design of blocked and split-plot experiments for fixed-effects and variance-components estimation (Presentation by Peter Goos @ Isaac Newton Institute, Cambridge (UK), August 31, 2011)

Eric Schoen on split-plot designs with factor-dependent whole-plot sizes (August 31, 2011)

In industrial split-plot experiments, the number of runs within each whole plot is usually determined independently from the factor settings. As a matter of fact, it is often equal to the number of runs that can be done within a given period of time or to the number of samples that can be processed in one oven run or with one batch. In such cases, the size of every whole plot in the experiment is fixed no matter what factor levels are actually used in the experiment. In this talk, we discuss the design of a real-life experiment on the production of coffee cream where the number of runs within a whole plot is not fixed, but depends on the level of one of the whole-plot factors. We provide a detailed discussion of various ways to set up the experiment and discuss how existing algorithms to construct optimal split-plot designs can be modified for that purpose. We conclude with a few general recommendations.

Peter Goos on optimal design of choice experiments in the presence of many attributes (August 17, 2011)

In a discrete choice experiment each respondent typically chooses the best product or service sequentially from many groups or choice sets of alternatives which are characterized by a number of different attributes. Respondents can find it difficult to trade off prospective products or services when every attribute of the offering changes in each comparison. Especially in studies involving many attributes, respondents get overloaded by the complexity of the choice task. To overcome respondent fatigue, it makes sense to simplify the comparison by holding some of the attributes constant in every choice set. A study in the health care literature where eleven attributes were allocated across three different experimental designs with only five attributes being varied motivates the approach we present. However, our algorithm is more general, allowing for any number of attributes and a smaller number of fixed attributes. We describe our algorithmic approach and show how the resulting design performed in our motivating example.

Eric Schoen on blocking orthogonal experimental designs (August 12, 2008)

Orthogonal arrays (OAs) of strength 2 permit independent estimation of main effects. An orthogonally blocked OA could be considered as an OA with one additional factor. Such an OA is in fact a two-stratum design. The main effects of the treatment factors are estimated in the bottom stratum. The upper stratum may contain interaction components for these factors. The blocking factor supposedly has no interactions with treatment factors. I propose to search for suitable blocking arrangements by studying projections of arrays into those with one factor less. I illustrate with a complete catalogue of blocked pure or mixed 18-run arrays.