### Multi-stratum response surface designs

Gilmour, S *(QMUL)*

Monday 11 August 2008, 14:00-14:30

Seminar Room 1, Newton Institute

#### Abstract

Many industrial and laboratory-based experiments involve studying some factors which are hard, time-consuming or expensive to change and other factors which can be changed more easily. It is now well-recognised that varying some factors more quickly than others leads to split-plot or other multi-stratum structures. When the aims of the experiment lead to a desire to fit second-order polynomial response surface models, it is usually impossible to use a standard orthogonal design. Instead, an algorithm is usually used to search for a design which is optimal in some way.
The different algorithms which have been suggested will be reviewed and the assumptions underlying their definitions of optimality will be reconsidered. The appropriateness of different criteria depend crucially on the objectives of the experiment and inappropriate scaling of the criteria can lead to misleading results. The differences and similarities between stratum-by-stratum and all-in-one methods of construction will be clarified. A Bayesian perspective will be used to show that, unless prior knowledge of the sizes of random effects is very certain or effects estimated in the higher strata are not of interest, experimenters should use either stratum-by-stratum methods or all-in-one methods with very large prior estimates of the higher stratum variance components.

#### Presentation

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