An extreme effect illustrated with the hexagonal design

16 An extreme effect illustrated with the hexagonal design 

Geometrically, the zero determinant arises because the number of FSOP models that can be made to pass through the responses above the hexagonal factor combinations is now truly infinite (see Section 5.6). There is no center point to define the apex and prevent the model from fluttering about. 

For purposes of illustration only, to circumvent the problem of a zero determinant but still show the distributions of uncertainty and information in this design, a seventh experiment was added at a factor combination just slightly removed from one of the hexagonal points (at jc, = 2.000, X2 = 0.001). The hexagonal points were also adjusted somewhat to coincide with the grid lines in the pseudo-three-dimensional plots (this is equivalent to a minor adjustment of scale in the X2 dimension). Neither of these modifications significantly affects the overall conclusions to be drawn from this example. The actual design is 

The striking feature of this design is the set of six spikes in both the normalized uncertainty and normalized information surfaces. These spikes are an extreme expression of the basic idea that experiments provide information. Even if the experimental design is not a good match for the model even if the iX X) matrix is ill conditioned even if the model doesn t fit the data very well, there is still high-quality information at the points where experiments have been carried out. 

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