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This paper discusses the treatment of uncertainties corresponding to relatively few samples of random-variable quantities. The importance of this topic extends beyond experimental data uncertainty to situations involving uncertainty in model calibration, validation, and prediction. With very sparse samples it is not practical to have a goal of accurately estimating the underlying variability distribution (probability density function, PDF). Rather, a pragmatic goal is that the uncertainty representation should be conservative so as to bound a desired percentage of the actual PDF, say 95% included probability, with reasonable reliability. A second, opposing objective is that the representation not be overly conservative; that it minimally over-estimate the random-variable range corresponding to the desired percentage of the actual PDF. The presence of the two opposing objectives makes the sparse-data uncertainty representation problem an interesting and difficult one.

As technical and non-technical constraints make testing of complex physical systems more restrictive, an increased reliance on modeling and simulation of large systems has arisen. Time and/or frequency domain analyzes of finite element models are performed on massively parallel computers. Due to the high consequence of these analyses, there is a need to quantitatively assess the predictive accuracy of finite element models used to simulate these complex physical systems relative to any available experimental results. In this paper we outline our understanding of model validation and the process followed to make a determination of the validity of a model. An example will be used to demonstrate the process.