Page 20 - Applied Statistics And Probability For Engineers

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6 CHAPTER 1 THE ROLE OF STATISTICS IN ENGINEERING

3. Production maintains the two temperatures as closely as possible to desired targets or
set points. Because the temperatures change so little, it may be difficult to assess their
real impact on acetone concentration.
4. Within the narrow ranges that they do vary, the condensate temperature tends to in-
crease with the reboil temperature. Consequently, the effects of these two process
variables on acetone concentration may be difficult to separate.

As you can see, a retrospective study may involve a lot of data, but that data may contain
relatively little useful information about the problem. Furthermore, some of the relevant
data may be missing, there may be transcription or recording errors resulting in outliers
(or unusual values), or data on other important factors may not have been collected and
archived. In the distillation column, for example, the specific concentrations of butyl alco-
hol and acetone in the input feed stream are a very important factor, but they are not
archived because the concentrations are too hard to obtain on a routine basis. As a result of
these types of issues, statistical analysis of historical data sometimes identify interesting
phenomena, but solid and reliable explanations of these phenomena are often difficult to
obtain.

1-2.3 Observational Study

In an observational study, the engineer observes the process or population, disturbing it as lit-
tle as possible, and records the quantities of interest. Because these studies are usually con-
ducted for a relatively short time period, sometimes variables that are not routinely measured
can be included. In the distillation column, the engineer would design a form to record the two
temperatures and the reflux rate when acetone concentration measurements are made. It may
even be possible to measure the input feed stream concentrations so that the impact of this fac-
tor could be studied. Generally, an observational study tends to solve problems 1 and 2 above
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 control-
lable 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 ex-
periment; that is, a deliberate change was made in the wall thickness of the connector with the
objective of discovering whether or not a greater pull-off force could be obtained. Designed
experiments play a very important role in engineering design and development and in the
improvement of manufacturing processes. Generally, when products and processes are designed
and developed with designed experiments, they enjoy better performance, higher reliability, and
lower overall costs. Designed experiments also play a crucial role in reducing the lead time for
engineering design and development activities.
For example, consider the problem involving the choice of wall thickness for the
nylon connector. 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