JMP 11 Online Documentation (English)
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Design of Experiments Guide
• Space-Filling Designs
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Space-Filling Designs
Space-filling designs are useful in situations where run-to-run variability is of far less concern than the form of the model. Sensitivity studies of computer simulations is one such situation. For this case, and any mechanistic or deterministic modeling problem, any variability is small enough to be ignored. For systems with no variability, randomization and blocking are irrelevant. Replication is undesirable because repeating the same run yields the same result. In space-filling designs, there are two objectives:
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Prevent replicate points by spreading the design points out to the maximum distance possible between any two points.
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Space the points uniformly.
The following methods are implemented for these types of designs:
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The Sphere-Packing method emphasizes spread of points.
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The Latin Hypercube method is a compromise between spread of points and uniform spacing.
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The Uniform method mimics the uniform probability distribution.
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The Minimum Potential method minimizes energy designs in a hypersphere.
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The Maximum Entropy method measures the amount of information contained in the distribution of a set of data.
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The Gaussian Process IMSE Optimal method creates a design that minimizes the integrated mean squared error of the gaussian process over the experimental region.
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The Fast Flexible Filling method locates points so that, for a given design size, the average distance from any point in the design region to the nearest design point is nearly minimized.
Space-Filling Design
Contents
Introduction to Space-Filling Designs
Sphere-Packing Designs
Creating a Sphere-Packing Design
Visualizing the Sphere-Packing Design
Latin Hypercube Designs
Creating a Latin Hypercube Design
Visualizing the Latin Hypercube Design
Uniform Designs
Comparing Sphere-Packing, Latin Hypercube and Uniform Methods
Minimum Potential Designs
Maximum Entropy Designs
Gaussian Process IMSE Optimal Designs
Fast Flexible Filling Designs
Creating a Constrained Fast Flexible Filling Design
Visualizing the Fast Flexible Filling Design
Borehole Model: A Sphere-Packing Example
Create the Sphere-Packing Design for the Borehole Data
Guidelines for the Analysis of Deterministic Data
Results of the Borehole Experiment