Applied Statistics and Probability for Engineers

506 CHAPTER 14 DESIGN OF EXPERIMENTS WITH SEVERAL FACTORS

6. Understand how two-level factorial designs can be run in blocks


7. Design and conduct two-level fractional factorial designs
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8. Incorporate random factors in factorial experiments.


9. Test for curvature in two-level factorial designs by using center points.


10. Use response surface methodology for process optimization experiments.

Answers for most odd numbered exercises are at the end of the book. Answers to exercises whose

numbers are surrounded by a box can be accessed in the e-text by clicking on the box. Complete

worked solutions to certain exercises are also available in the e-Text. These are indicated in the

Answers to Selected Exercises section by a box around the exercise number. Exercises are also

available for some of the text sections that appear on CD only. These exercises may be found in the

Mind-Expanding Exercises at the end of the chapter.

14-1 INTRODUCTION

An experimentis just a testor series of tests. Experiments are performed in all engineering and

scientific disciplines and are an important part of the way we learn about how systems and

processes work. The validity of the conclusions that are drawn from an experiment depends to a

large extent on how the experiment was conducted. Therefore, the designof the experiment

plays a major role in the eventual solution of the problem that initially motivated the experiment.

In this chapter we focus on experiments that include two or more factors that the experi-

menter thinks may be important. The factorial experimental designwill be introduced as a

powerful technique for this type of problem. Generally, in a factorial experimental design, ex-

perimental trials (or runs) are performed at all combinations of factor levels. For example, if

a chemical engineer is interested in investigating the effects of reaction time and reaction tem-

perature on the yield of a process, and if two levels of time (1 and 1.5 hours) and two levels of

temperature (125 and 150F) are considered important, a factorial experiment would consist

of making experimental runs at each of the four possible combinations of these levels of reac-

tion time and reaction temperature.

Most of the statistical concepts introduced in Chapter 13 for single-factor experiments

can be extended to the factorial experiments of this chapter. The analysis of variance

(ANOVA), in particular, will continue to be used as one of the primary tools for statistical data

analysis. We will also introduce several graphical methods that are useful in analyzing the data

from designed experiments.

14-2 SOME APPLICATIONS OF DESIGNED EXPERIMENTS

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14-3 FACTORIAL EXPERIMENTS

When several factors are of interest in an experiment, a factorial experimental designshould

be used. As noted previously, in these experiments factors are varied together.

By a factorial experimentwe mean that in each complete trial or replicate of the

experiment all possible combinations of the levels of the factors are investigated.

Definition

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