Chemistry Reference
In-Depth Information
CHAPTER 13
Design of Experiments and Statistical
Process Control
13.1 INTRODUCTION
The topics of this chapter involve a certain amount of mathematics and many
associated texts are full of mind-numbing pages of equations. The object here
is to introduce the reader to the subjects, explain their importance and give
some sense of how they are used. Some use of mathematics is necessary,
but every attempt will be made to keep the examples simple so we can keep
focused on the larger picture of why these techniques are useful.
In the discussion of pharmaceuticals and the importance of standard operat-
ing procedures, an example involving the flying of paper airplanes was used.
Curious as to my talent in such an endeavor, I armed myself with several
sheets of white copy paper and went to an empty classroom on the first floor.
I assembled and flew four paper airplanes and each time carefully measured
the flight distance. They flew 12.7, 13.1, 12.5, and 13.0 feet. A bar chart
(Figure 13.1) can be easily made.
The average or mean can be calculated by the sum of the individual mea-
surements divided by the number of measurements. In this case, the four
flights totaled 51.3 feet, which upon dividing by 4 gives 12.825 feet as the
average. Because each of the measurements was done to a precision of three
significant figures, strictly speaking the average should also be reported to
the same level of precision, namely 12.8 feet. Note that the number “4” in
this example is an exact number (there were exactly 4 flights) so this does not
imply a precision of one significant figure.
We can get some idea of the variability of these numbers by calculating the
standard deviation. The standard deviation is the square root of the variance.
The variance is the sum of the squares of the difference of each value from the
mean divided by the number of samples. By squaring the numbers, the sign
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