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William Li, Principal Investigator and Christopher J. Nachtsheim, Co-Principal Investigator

Model Robust Response Surface Design

An important issue in both research and manufacturing areas is how to design experiments for the most efficient use of resources. Today, the need to reduce cost has led to the use of designs that cannot be easily constructed in a traditional way. Experimental designs used in modern industry usually allow for fewer runs, which has partly motivated the advances in optimal design algorithms. Optimal designs have been widely used in history. However, one of the major concerns is that they are only "optimal" with respect to certain criteria based on a model. Thus, their optimality is dependent on how accurate the model assumption is. When the true model is different from the original assumption, the "optimal design" based on that assumption is no longer optimal and may even perform poorly. Thus, it is important to investigate model robust designs-designs performing well against a variety of models.

Recent interest has focused on the construction of two-level factorial experiments. A framework had been established for assessing the capability of factorial experimental designs for estimating various models with main effects and interactions. It was desirable to find factorial designs with good model robustness properties. This approach identifies model robust designs selected among orthogonal designs. This is a major limitation since orthogonal designs with one hundred percent of estimation capacity may not exist. Even when they exist, they may perform poorly with respect to other model robust criteria.

This research has already found that a slight sacrifice of orthogonality may greatly improve design performance in terms of model robustness. A new algorithm has been proposed for constructing optimal model robust, two-level factorial designs. A general model robust design criterion has also been described.

The current objective of this study is to extend this research to the construction of model robust response surface designs. In earlier work, the model space included two-level designs with all main effects and some two-factor interactions. In practice, many examples include non-linear effects that cannot be captured by a two-level design. A traditional approach is to use response surface designs. Standard response surface designs, such as small central composite designs, may not perform well against all possible models in a model space. An algorithm is now being developed for constructing response surface designs whose design space consists of not only linear effects but also quadratic and interaction terms.

This information is available in alternative formats upon request by individuals with disabilities. Please send email to alt-format@msi.umn.edu or call 612-624-0528.

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