Kriging models have proven useful in estimating complex and computationally expensive analyses. They are capable of interpolating a set of observations by quantifying both longer range variations with parametric trends and shorter range variations with spatial correlations. Kriging models have had some difficulty with robustness in situations when there are a larger number of input dimensions and few observations as well as a larger number of observations with few dimensions. This paper will detail how to add a parameter to the kriging model that will account for random or measurement errors. The result is a model that will no longer interpolate all of the observations and may be a function of fewer of input dimensions. The resulting model may be better able to approximate the orignal function as demonstrated in four two-dimensional examples.