Page 21 - Applied Statistics And Probability For Engineers

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1-2 COLLECTING ENGINEERING DATA 7

engineer is interested in determining if there is any difference between the 3 32- and
1 8-inch designs. An approach that could be used in analyzing the data from this experi-
ment is to compare the mean pull-off force for the 3 32-inch design to the mean pull-off
force for the 1 8-inch design using statistical hypothesis testing, which is discussed in
detail in Chapters 9 and 10. Generally, a hypothesis is a statement about some aspect of the
system in which we are interested. For example, the engineer might want to know if the
mean pull-off force of a 3 32-inch design exceeds the typical maximum load expected to
be encountered in this application, say 12.75 pounds. Thus, we would be interested in test-
ing the hypothesis that the mean strength exceeds 12.75 pounds. This is called a single-
sample hypothesis testing problem. It is also an example of an analytic study. Chapter 9
presents techniques for this type of problem. Alternatively, the engineer might be inter-
ested in testing the hypothesis that increasing the wall thickness from 3 32- to 1 8-inch
results in an increase in mean pull-off force. Clearly, this is an analytic study; it is also an
example of a two-sample hypothesis testing problem. Two-sample hypothesis testing
problems are discussed in Chapter 10.
Designed experiments are a very powerful approach to studying complex systems, such
as the distillation column. This process has three factors, the two temperatures and the reflux
rate, and we want to investigate the effect of these three factors on output acetone concentra-
tion. A good experimental design for this problem must ensure that we can separate the effects
of all three factors on the acetone concentration. The specified values of the three factors used
in the experiment are called factor levels. Typically, we use a small number of levels for each
factor, such as two or three. For the distillation column problem, suppose we use a “high,’’ and
“low,’’ level (denoted +1 and 1, respectively) for each of the factors. We thus would use two
levels for each of the three factors. A very reasonable experiment design strategy uses every
possible combination of the factor levels to form a basic experiment with eight different set-
tings for the process. This type of experiment is called a factorial experiment. Table 1-1 pres-
ents this experimental design.
Figure 1-6, on page 8, illustrates that this design forms a cube in terms of these high and
low levels. With each setting of the process conditions, we allow the column to reach equilib-
rium, take a sample of the product stream, and determine the acetone concentration. We then
can draw specific inferences about the effect of these factors. Such an approach allows us to
proactively study a population or process. Designed experiments play a very important role in
engineering and science. Chapters 13 and 14 discuss many of the important principles and
techniques of experimental design.

Table 1-1 The Designed Experiment (Factorial Design) for the
Distillation Column

Reboil Temp. Condensate Temp. Reflux Rate
1 1 1
1 1 1
1 1 1
1 1 1
1 1 1
1 1 1
1 1 1
1 1 1