Design of Experiments Guide • Space-Filling Designs • Minimum Potential Designs
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Minimum Potential Designs
The Minimum Potential design spreads points out inside a sphere. To understand how this design is created, imagine the points as electrons with springs attached to every other point, as illustrated to the right. The coulomb force pushes the points apart, but the springs pull them together. The design is the spacing of points that minimizes the potential energy of the system.
Minimum Potential Design
Minimum Potential designs:
•
have spherical symmetry
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are nearly orthogonal
•
have uniform spacing
To see a Minimum Potential example:
1.
Select DOE > Space Filling Design.
2.
Add 1 continuous factor.
See Factors.
3.
Alter the factor level values to 0 and 1, if necessary.
4.
Click Continue.
5.
In the design specification dialog (shown on the left in Space-Filling Methods and Design Diagnostics for Minimum Potential Design), enter a sample size (Number of Runs). This example uses a sample size of 12.
6.
Click the Minimum Potential button. JMP creates this design and displays the design runs and the design diagnostics (shown on the right in Space-Filling Methods and Design Diagnostics for Minimum Potential Design).
Space-Filling Methods and Design Diagnostics for Minimum Potential Design
7.
Click Make Table.
You can see the spherical symmetry of the Minimum Potential design using the Scatterplot 3D graphics platform.
1.
After you make the JMP design table, choose the Graph > Scatterplot 3D command.
2.
In the Scatterplot 3D launch dialog, select X1, X2, and X3 as Y, Columns and click OK to see the initial three-dimensional scatterplot of the design points.
3.
To see the results similar to those in Minimum Potential Design Points on Sphere:
‒
Select the Normal Contour Ellipsoids option from the menu in the Scatterplot 3D title bar.
‒
Make the points larger. Right-click on the plot and select Settings, and then increase the Marker Size slider.
Now it is easy to see the points spread evenly on the surface of the ellipsoid.
Minimum Potential Design Points on Sphere