22. September 2014

The advantage of space-filling designs of experiments

Space-filling designs of experiments guarantee an optimal coverage of the experimental space.

To analyze characteristics of processes and products data is required. In many cases there is no data directly available. Therefore, to reach the best possible coverage of the different process states or product features, special designs of experiments are used. For this purpose there are many applications from statistics, for example so-called factorial designs of experiments or Latin Hyper Squares.

Unfortunately, these designs are not able to suitably take into account already existing data points or constraints. For example, if there were a constraint x1 + x2 ? 1.5, the plan shown in figure 2 would remove the invalid points.

In these cases space-filling designs are advantageous. These plans are based on the fact that the points are moved iteratively in the experimental space, so that the minimal distance of one point to the next is maximized. Constrants and already existing data points are also taken into account. This guarantees an optimal coverage of the experimental space.

Fig. 1: 2-dimensional LHS design with 32 data points
Fig. 2: LHS design with constraints
Fig. 3: 2-dimensional space-filling design with 32 data points