Design and Analysis of Experiments, 9th Edition

CHAPTER 7Blocking and Confounding in the 2^k Factorial Design

CHAPTER OUTLINE

1. 7.1 INTRODUCTION
2. 7.2 BLOCKING A REPLICATED 2^k FACTORIAL DESIGN
3. 7.3 CONFOUNDING IN THE 2^k FACTORIAL DESIGN
4. 7.4 CONFOUNDING THE 2^k FACTORIAL DESIGN IN TWO BLOCKS
5. 7.5 ANOTHER ILLUSTRATION OF WHY BLOCKING IS IMPORTANT
6. 7.6 CONFOUNDING THE 2^k FACTORIAL DESIGN IN FOUR BLOCKS
7. 7.7 CONFOUNDING THE 2^k FACTORIAL DESIGN IN 2^p BLOCKS
8. 7.8 PARTIAL CONFOUNDING

SUPPLEMENTAL MATERIAL FOR CHAPTER 7

1. S7.1 The Error Term in a Blocked Design
2. S7.2 The Prediction Equation for a Blocked Design
3. S7.3 Run Order Is Important

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

CHAPTER LEARNING OBJECTIVES

1. Learn about how the blocking technique can be used with 2^k factorial designs.
2. Learn about how blocking can be used with unreplicated 2^k factorial designs, and how this leads to confounding of effects.
3. Know how to construct the 2^k factorial designs in 2^p blocks.
4. Understand how to construct designs that confound different effects in different replicates.

7.1 Introduction

In many situations it is impossible to perform all of the runs in a $2^k$ factorial experiment under homogeneous conditions. For example, a single batch of raw material might not be large enough to make all of the required runs. In other cases, it might be desirable to deliberately vary the experimental conditions to ensure that the treatments are equally effective (i.e., robust) across many situations that are likely to be ...