Page 28 - Applied statistics and probability for engineers

6 Chapter 1/The Role of Statistics in Engineering

Generally, an observational study tends to solve problems 1 and 2 and goes a long way
toward obtaining accurate and reliable data. However, observational studies may not help
resolve problems 3 and 4.

1-2.4 DESIGNED EXPERIMENTS
In a designed experiment, the engineer makes deliberate or purposeful changes in the controlla-
ble variables of the system or process, observes the resulting system output data, and then makes
an inference or decision about which variables are responsible for the observed changes in output
performance. The nylon connector example in Section 1-1 illustrates a designed experiment;
that is, a deliberate change was made in the connector’s wall thickness with the objective of dis-
covering whether or not a stronger pull-off force could be obtained. Experiments designed with
basic principles such as randomization are needed to establish cause-and-effect relationships.
Much of what we know in the engineering and physical-chemical sciences is developed
through testing or experimentation. Often engineers work in problem areas in which no scien-
tiic or engineering theory is directly or completely applicable, so experimentation and obser-
vation of the resulting data constitute the only way that the problem can be solved. Even when
there is a good underlying scientiic theory that we may rely on to explain the phenomena of
interest, it is almost always necessary to conduct tests or experiments to conirm that the the-
ory is indeed operative in the situation or environment in which it is being applied. Statistical
thinking and statistical methods play an important role in planning, conducting, and analyzing
the data from engineering experiments. Designed experiments play a very important role in
engineering design and development and in the improvement of manufacturing processes.
For example, consider the problem involving the choice of wall thickness for the nylon connec-
tor. This is a simple illustration of a designed experiment. The engineer chose two wall thicknesses
for the connector and performed a series of tests to obtain pull-off force measurements at each
wall thickness. In this simple comparative experiment, the engineer is interested in determining
whether 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 experiment 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 testing the
hypothesis that the mean strength exceeds 12.75 pounds. This is called a single-sample hypothesis-
testing problem. Chapter 9 presents techniques for this type of problem. Alternatively, the engineer
might be interested 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. It is an example of a two-sample hypothesis-testing
problem. Two-sample hypothesis-testing problems are discussed in Chapter 10.
Designed experiments offer a very powerful approach to studying complex systems, such
as the distillation column. This process has three factors—the two temperatures and the relux
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 speciied values of the three factors used
in the experiment are called factor levels. Typically, we use a small number of levels such as
two or three for each factor. For the distillation column problem, suppose that we use two lev-
els, “high’’ and “low’’ (denoted +1 and -1, respectively), 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 settings for the process. This type of experiment
is called a factorial experiment. See Table 1-1 for this experimental design.
Figure 1-5 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 equilibrium, take
a sample of the product stream, and determine the acetone concentration. We then can draw