Kriging as an alternative to polynomial regression in response surface analysis
Response surface methodology (RSM) is typically used in the modeling and optimization of processes. RSM relies upon empirical approximations of true process relationships, with the second order polynomial model being the most popular. Structured designs, such as Central Composite or Box-Behnken, are used for data collection and subsequent parameter estimates in these models are traditionally found via ordinary least squares methods. One common difficulty in RSM is lack of fit resulting from an under-specified model, which can lead to biased estimates for the parameters and incorrect estimates of the process maximum. One solution to this problem is the use of Box-Cox transformations on the data. As an alternative, kriging will be presented as a viable method for modeling near quadratic surfaces. Kriging is a spatial statistics method, first developed for applications in the mining industry, whose basic premise is the use of a weighted average of local data points to predict a new response. Two kriging methods, Ordinary and Universal, will be evaluated for various surfaces in 1, 2, & 3 dimensions.