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418 Chapter Twelve

If the confirmation runs don’t produce the results you expected, then
you need to

1. Check to see that nothing has changed since the original data
collection.
2. Verify that you have the correct settings for the confirmation runs.
3. Revisit the model to verify the “best” settings from the analysis.
4. Verify that you had the correct predicted value for the confirmation
runs.
If you don’t find the answer after checking these four items, the model
may not predict very well in the region that you decided was “best.”
However, you still will have learned something from the experiment, and
you should use the information gained from this experiment to design
another follow-up experiment.

12.2 Factorial Experiment

Most industrial experiments involve two or more experimental factors.
In this case, factorial designs are the most frequently used designs. By
a factorial design, we mean that all combinations of factor levels will
be tested in the experiment. For example, we have two factors in the
experiment, say, factors A and B. If A has a levels, B has b levels, then
in a factorial experiment, we are going to test all ab combinations. In
each combination, we may duplicate the experiment several times, say,
n times. Then, there are n replicates in the experiment. If n 1, then
we call it a single replicate. Therefore, for two factors, the total num-
ber of experimental observations is equal to abn.

Example 12.2 An article in Industrial Quality Control (1956, vol. 13, no. 1,
pp. 5–8) describes an experiment to investigate the effect of the type of
glass and the type of phosphor on the brightness of a television tube. The
response variable is the current necessary (in microamps) to obtain a spe-
cific brightness level. The data are listed in Table 12.1.In this example, we
can call the glass type factor A, so the number of A levels is a 2; the
phosphor type, factor B, with b 3 as the number of B levels. The num-
ber of replicates in this example is n 3. Total experimental observations
2
3
3 18 runs. Both glass and phosphor types are discrete factors.
We would like to determine the following:
1. How the glass and phosphor types will affect the brightness of the TV,
and whether these effects, if any, are significant, and whether there are any
interactions.
2. Y is defined to be the current needed to achieve a certain brightness level,
so the smaller current means higher efficiency. We would like to find a glass-
phosphor combination that gives the best efficiency.
Data analysis for this example is given in Example 12.4.