Page 30 - Applied statistics and probability for engineers

8 Chapter 1/The Role of Statistics in Engineering

Column design
Old New Condensate temperature
Reflux rate 11 11
FIGURE 1-6 A 21 21
four-factorial
21 11
experiment for the
distillation column. Reboil temperature

Factorial and fractional factorial experiments are used extensively by engineers and scientists in
industrial research and development, where new technology, products, and processes are designed
and developed and where existing products and processes are improved. Since so much engineer-
ing work involves testing and experimentation, it is essential that all engineers understand the basic
principles of planning eficient and effective experiments. We discuss these principles in Chapter
13. Chapter 14 concentrates on the factorial and fractional factorials that we have introduced here.

1-2.5 Observing Processes Over Time

Often data are collected over time. In this case, it is usually very helpful to plot the data versus
time in a time series plot. Phenomena that might affect the system or process often become
more visible in a time-oriented plot and the concept of stability can be better judged.
Figure 1-8 is a dot diagram of acetone concentration readings taken hourly from the distil-
lation column described in Section 1-2.2. The large variation displayed on the dot diagram
indicates considerable variability in the concentration, but the chart does not help explain the
reason for the variation. The time series plot is shown in Fig. 1-9. A shift in the process mean
level is visible in the plot and an estimate of the time of the shift can be obtained.
W. Edwards Deming, a very inluential industrial statistician, stressed that it is important
to understand the nature of variability in processes and systems over time. He conducted an
experiment in which he attempted to drop marbles as close as possible to a target on a table.
He used a funnel mounted on a ring stand and the marbles were dropped into the funnel. See
Fig. 1-10. The funnel was aligned as closely as possible with the center of the target. He then
used two different strategies to operate the process. (1) He never moved the funnel. He just
dropped one marble after another and recorded the distance from the target. (2) He dropped
the irst marble and recorded its location relative to the target. He then moved the funnel an
equal and opposite distance in an attempt to compensate for the error. He continued to make
this type of adjustment after each marble was dropped.
Unnecessary After both strategies were completed, he noticed that the variability of the distance from the
Adjustments Can target for strategy 2 was approximately twice as large than for strategy 1. The adjustments to
Increase Variability the funnel increased the deviations from the target. The explanation is that the error (the devia-
tion of the marble’s position from the target) for one marble provides no information about
the error that will occur for the next marble. Consequently, adjustments to the funnel do not
decrease future errors. Instead, they tend to move the funnel farther from the target.

Column design

Old New
Reflux rate 11
FIGURE 1-7 A 11 Condensate temperature
fractional factorial 21 21
experiment for the
21 11
connector wall
thickness problem. Reboil temperature