Identifying rising ridge behavior in quadratic response surfaces

Canonical analysis is a common method for exploring and exploiting fitted quadratic response surfaces. Much attention in canonical analysis is given to identifying ridge behavior in these surfaces in order to achieve optimal response at minimum cost. However, little attention has been given to classifying the identified ridge as a stationary ridge or a rising ridge. Knowing whether a ridge is stationary or rising is critical for making decisions about how to continue the response surface exploration or for setting process parameters. This article presents two methods that allow for identification, classification and confirmation of ridge behavior. The first method is based on linear regression and though easily implemented, can be imprecise. The second method is more precise and is based on a new parameterization of the canonical form. It uses nonlinear regression techniques that are becoming increasingly accessible through software packages.