A Gumbel Distribution Model to Describe Correlation Values in Random Latin Hypercube Experimental Designs for Model and Simulation Based Systems Engineering
Alejandro S. Hernandez

Experimentation is critical for trade-off analysis during design and development, as well as test phases of model based or model and simulation based systems engineering, or use of simulation based designs. Latin hypercube designs are effective experimental schemes that can save time and resources. However, they can also have highly correlated columns that present problems during post simulation analysis. Experimenters need a means to know if the Latin hypercube design that they plan to generate has a tolerable amount of correlation within its columns. A known probability model greatly aids this need. Application of the Kolmogorov-Smirnov goodness-of-fit tests shows the appropriateness of the Type 1 Gumbel distribution to model the smallest maximum absolute pair wise correlation from a set of random Latin hypercube experimental designs with equal dimensions (design points and factors). We estimate the Gumbel’s location and dispersion parameters using only information from the design environment. Results of this paper improve the scientist’s ability to plan better experiments for the specific study condition.

Full Text: PDF     DOI: 10.15640/jea.v4n2a1