Models, Uncertainty, and the Sandia V&V Challenge Problem

In this paper, we argue that the Sandia V&V Challenge Problem is ill-posed in that the answers sought do not, mathematically, exist. This effectively discredits both the methodologies applied to the problem and the results, regardless of the approach taken. We apply our arguments to show the types of mistakes present in the papers presented in J. of VVUQ along with the Challenge Problem. Further, we show that, when the problem is properly posed, both the applicable methodology and the solution techniques are easily drawn from the well-developed mathematics of probability and decision theory. The unfortunate aspect of the Challenge Problem as currently stated is that it leads to incorrect and inappropriate mathematical approaches that should be avoided and corrected in the current literature.