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

Chapter 18

The 2^k Factorial Designs

The focus of this chapter is the development of special experimental designs involving factors having two levels each. The topics covered are:

• The factorial designs
• The 2^k factorial designs
• Unreplicated 2^k factorial designs
• Blocking the 2^k factorial designs
• Confounding in the 2^k factorial designs
• Yates’ algorithm for the 2^k factorial designs
• The 2^k fractional factorial designs
• One-half replication of a 2^k factorial design
• One-quarter replication of a 2^k factorial design

Learning Outcomes:

After studying this chapter, the reader will be able to

• Design and conduct special kinds of experiments in engineering or other scientific fields involving two or more factors.
• Create blocking appropriately to avoid any kind of confounding.
• Create blocking using appropriate interactions when experiments are designed using only one-half or one-quarter replication of a 2^k design.
• Analyze data coming out of experiments employing some special techniques.
• Perform residual analysis to check the adequacy of the models under consideration.
• Summarize and interpret the results of these experiments.
• Use statistical packages MINITAB, Microsoft Excel, and JMP to analyze the data in these experiments.

Introduction

We continue our discussion of factorial designs that began in Chapter 17. In this chapter we consider an important class of factorial designs in which each of the k factors has only two levels. Since these designs have exactly 2^k treatments, they are usually ...