Optimization Of First Order Models

In Response Surface Methods, the optimal region to run a process is usually determined after a sequence of experiments is conducted and a series of empirical models are obtained. As mentioned in Chapter 1, in a new or poorly understood process it is likely that a first order model will fit well. The Box-Wilson methodology suggests the use of a steepest ascent technique coupled with lack of fit and curvature tests to move the process from a region of little curvature to one where curvature – and the presence of a stationary point – exists. In this chapter we discuss, at an elementary level, steepest ascent/descent methods for optimizing a process described by a first order model. We will assume readers are familiar with the linear regression material reviewed in Appendix A. More advanced techniques related to exploring a new region that incorporate the statistical inference issues into the optimization methods are discussed in Chapter 6.