Design of Experiments and Statistical Process Control - Fundamentals of Industrial Chemistry: Pharmaceuticals, Polymers, and Business - page 231

this design. By planning the experiments, we are able to do fewer experiments
and gain more information.
Consider an example with three variables, e.g. perhaps in a synthesis, time,
temperature, and catalyst loading, would be important variables. The design
of experiments would vary these three variables and be called a three-factor
design or a three-way design. Often they are varied at two levels, the practical
extremes. Perhaps the temperature would be studied at 20 ∘ C and 90 ∘ C, the
time at 1 hour and 6 hours and the catalyst loading at 50 ppm and 500 ppm.
Each of these extremes would be chosen by the experimenter as what makes
sense for the reaction. Because two levels are being studied, this design is
a three-factor design with two levels. Completion of a full factorial design
would require all of the combinations to be tested. For a three-factor design
with two levels, there are 2 3

8 combinations and this might be called a 2 3 full
factorial design. Analysis of the data allows the experimenter to understand
interactions and main effects. The experiments should be done in random
order to avoid being misled by any unknown variables such as improving pro-
ficiency in the synthesis or deteriorating purity of one of the raw materials.
It is also helpful to include one or two replicates and perhaps a center point
such as medium temperature, time, and catalyst loading. If you plan ten exper-
iments, labeling them from one to ten, you can simply write the ten numbers
on slips of paper, shake them in a jar or hat and pull them out; performing the
experiments in the order you pick them from the jar.
There are software packages available that will help design the experi-
ments, give an order for their execution, help with the data interpretation,
and print graphs with the results. As with any software, it is important for the
scientist to avoid abdication of all reasoning to the computer. It is important
for the scientist to think about the experiments and the results and make sure
they are consistent with scientific principles. Early in his career, the author
consulted with the company statistician who employing software guided the
experimental design for the reaction of bromine with acetone to synthesize
1,1,3- tribromoacetone. After the design was performed, the statistician con-
sulted the computer analysis of the results and declared that bromine was
not necessary. Any chemist recognizes that this is wrong. The effect was
parabolic and our levels were at opposite sides of the parabola. This confusion
would have been eliminated by choosing to do a center point experiment, but
nonetheless illustrates the importance of thinking about the science behind
any observations.
Often there are many more than three important variables. Even with only
five variables, we are at 2 5

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32 experiments for a full factorial design. We
would prefer to also have a center point and one or two replicates, so now we
are at 35. Dependent upon the difficulty in performing each experiment, this
can be a large undertaking. One option is to undertake a fractional factorial

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