Statistics and Probability with Applications for Engineers and Scientists Using MINITAB, R and JMP, 2nd Edition

Chapter 19Response Surfaces

The focus of this chapter is the development of first‐order and second‐order (central composite) designs employed for fitting response surfaces.

Topics Covered

• First‐order designs
• Second‐order designs
• Central composite designs (CCDs)
• 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.
• Use statistical packages MINITAB, R, and JMP to analyze response surface.

19.1 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 , , …, . The ...