Space-filling designs are useful for modeling systems that are deterministic or near-deterministic. One example of a deterministic system is a computer simulation. Such simulations can be very complex involving many variables with complicated interrelationships. A goal of designed experiments on these systems is to find a simpler empirical model that adequately predicts the behavior of the system over limited ranges of the factors.
In experiments on systems where there is substantial random noise, the goal is to minimize the variance of prediction. In experiments on deterministic systems, there is no variance but there is bias. Bias is the difference between the approximation model and the true mathematical function. The goal of space-filling designs is to bound the bias.
There are two schools of thought on how to bound the bias. One approach is to spread the design points out as far from each other as possible consistent with staying inside the experimental boundaries. The other approach is to space the points out evenly over the region of interest.
The Space Filling designer supports the following design methods:
Note: If the number of runs is 500 or less, a Gaussian Process model is saved to the data table. If the number of runs exceeds 500, a Neural model is saved to the data table.
maximizes the minimum distance between design points but requires even spacing of the levels of each factor. This method produces designs that mimic the uniform distribution. The Latin Hypercube method is a compromise between the Sphere-Packing method and the Uniform design method.
minimizes the discrepancy between the design points (which have an empirical uniform distribution) and a theoretical uniform distribution.
creates a design that minimizes the integrated mean squared error of the Gaussian process over the experimental region.
uses cluster methods to construct a design that places a design point close to any point in the design region. Accommodates linear constraints and disallowed combinations on the design space. You can construct linear constraints using the Linear Constraint button. You can specify Disallowed Combinations by selecting that option from the report’s red triangle menu. See Disallowed Combinations: Accounting for Factor Level Restrictions.