Statistics and Probability with Applications for Engineers and Scientists, Preliminary Edition

Chapter 19

Response Surfaces

The focus of this chapter is the development of first-order and second-order (central composite) designs employed for fitting response surfaces. The topics covered are:

• First-order designs
• Second-order designs
• Central composite designs (CCD)
• Some other first-order and second-order designs
• Determination of the optimum or near optimum point
• The method of steepest ascent
• Analysis of a fitted second-order response surface

Learning Outcomes:

After studying this chapter, the reader will be able to

• Select appropriate designs to fit-first-order and second-order models.
• Use the least-squares method to fit a desired model.
• Use analysis of variance techniques to verify the adequacy of the fitted models.
• Analyze the fitted response surface to determine the nature of the response surface.
• Use certain techniques to determine the optimum (or near-optimum) point of the response surface.

Introduction

Response surface methodology (RSM) allows an experimenter to explore an unknown functional relationship between a response variable Y and k controlled or independent variables, say ξ₁, ξ₂,..., ξ_k. The method was introduced by Box and Wilson (1951). The main goals of RSM are to use a sequence of planned experiments to seek an optimal response and to assess a functional relationship in the neighborhood of the optimal response. In this chapter we study various commonly used response surface designs and their analysis.

19.1 Basic Concepts of Response Surface Methodology ...