Guiding Construction of Better Test Designs by Modeling Random Latin Hypercube Correlation Values with the Gumbel Distribution

摘要

The operational test and evaluation community can gain significant benefits from using efficient experimental designs in their test regimen. While there are a variety of design schemes from which to choose, analysts have increasingly used Latin hypercube designs for experiments. However, these designs can have sizable correlations among columns of the design matrix, which can cause significant errors in estimates from the resultant data. A probability model that describes the behavior of correlation values of random Latin hypercubes can assist the analyst construct better experiments. This paper employs the Kolmogorov-Smirnov goodness-of-fit tests to show the appropriateness of the Type 1 or minimum Gumbel distribution to model the smallest maximum absolute pairwise correlation from a set of same-sized, random Latin hypercubes. We accurately estimate the Gumbel's location and dispersion parameters by only using the information from the design environment. The resulting model enables scientists to improve their construction of an experiment that fits the study condition and facilitates increased credibility in post analysis.