Design and Analysis of Experiments, 9th Edition

CHAPTER 6The 2^k Factorial Design

CHAPTER OUTLINE

1. 6.1 INTRODUCTION
2. 6.2 THE 2² DESIGN
3. 6.3 THE 2³ DESIGN
4. 6.4 THE GENERAL 2^k DESIGN
5. 6.5 A SINGLE REPLICATE OF THE 2^k DESIGN
6. 6.6 ADDITIONAL EXAMPLES OF UNREPLICATED 2^k DESIGNS
7. 6.7 2^k DESIGNS ARE OPTIMAL DESIGNS
8. 6.8 THE ADDITION OF CENTER POINTS TO THE 2^k DESIGN
9. 6.9 WHY WE WORK WITH CODED DESIGN VARIABLES

SUPPLEMENTAL MATERIAL FOR CHAPTER 6

1. S6.1 Factor Effect Estimates Are Least Squares Estimates
2. S6.2 Yates's Method for Calculating Factor Effects
3. S6.3 A Note on the Variance of a Contrast
4. S6.4 The Variance of the Predicted Response
5. S6.5 Using Residuals to Identify Dispersion Effects
6. S6.6 Center Points Versus Replication of Factorial Points
7. S6.7 Testing for “Pure Quadratic” Curvature Using a t-Test

The supplemental material is on the textbook website www.wiley.com/college/montgomery.

CHAPTER LEARNING OBJECTIVES

1. Learn about the 2^k series of factorial designs.
2. Know how to compute main effects and interactions for 2^k factorial designs.
3. Learn how the analysis of variance can be used for 2^k factorial designs.
4. Know how to represent the results from a 2^k factorial design as a regression model.
5. Know how to use graphical and analytical methods to analyze unreplicated 2^k factorial designs.
6. Understand the basics of design optimality: D-optimality, I-optimality, and G-optimality, and why factorial designs are generally optimal designs.
7. Know how to use design optimality criteria in constructing designs.
8. Know the value of adding center runs ...