Design Points (Vertices & Centroids) for Constrained Surfaces and Mixtures - Options Tab

Standard Designs for Mixture Experiments

Select the Options tab of the Design Points (Vertices & Centroids) for Constrained Surfaces and Mixtures dialog to access options to control some of the technical parameters of the algorithm for finding the vertex points for the constrained region.

Tolerance (delta) for checking

Use the options in the Tolerance (delta) for checking group box to check whether a particular constraint is violated and whether two points are identical. Enter values in the appropriate fields or use the microscrolls to specify the tolerance level to use.

As described in the Introductory Overview, the Experimental Design module uses a general algorithm proposed by Piepel (1988) and Snee (1979; the general approach is also described in detail in Snee, 1979). Specifically, Statistica considers each linear constraint one by one. Each constraint represents a line (or plane) through the experimental region. For each successive constraint, Statistica  evaluates whether or not the current (new) constraint crosses into the current valid region of the design. If so, new vertices will be computed which define the new valid experimental region, updated for the most recent constraint. Statistica then checks whether or not any of the previously processed constraints have become obsolete, that is, define lines or planes in the experimental region that are now entirely outside the valid region.

Constraints

The value in the Constraints box determines the precision used by Statistica when determining whether constraints are incompatible. Because the algorithm implemented in Statistica performs all computations in the highest floating point precision, usually you do not need to change the parameter (however, it is recommended that you scale the factors in the analysis to compatible orders of magnitude).

For duplicate points

The value in the For duplicate points box determines the precision used by Statistica when determining whether or not two or more vertex points are redundant. Because the algorithm implemented in Statistica performs all computations in the highest floating point precision, usually you do not need to change these parameters (however, it is recommended that you scale the factors in the analysis to compatible orders of magnitude).

Maximum size (memory) of problem

When you process large problems with many factors and constraints, the number of vertex points can become quite large. In those cases, when you select to compute centroid points for several low dimensions, the number of centroid points can become substantial. Use the options in the Maximum size (memory) of problem group box to be alerted of the number of vertex and centroid points as they are generated.

Dynamically grow memory as needed

If the Dynamically grow memory as needed check box is selected, Statistica "makes room" for vertex and centroid points as they are generated. However, when there are several thousand vertex points, the size of the design can get so large that the computations become very slow. To alert you of a situation where a large number of vertex points (and more centroid points) are necessary to describe the experimental region, you can clear the Dynamically grow memory as needed check box to make the Maximum number of vertices and Maximum number of centroids boxes available.

Maximum number of vertices

Statistica issues a warning when the limit specified in the Maximum number of vertices box has been exceeded. Usually, if there are, for example, more than 1,000 vertex points, it is advisable to break down the problem, and to introduce fewer constraints, involving fewer factors at a time.

Maximum number of centroids

Statistica issues a warning when the limit specified in the Maximum number of centroids box has been exceeded.