Discussion on the Split-Plot Experiment of Table 14-14 on pp. 540542 of Montgomery’s 6th Edition
By S. Maghsoodloo
First, bear in mind that the primary objective of a split-plot design is to
randomize the levels of the hardest-to-change factor at stage 1 (this is the one
restriction on randomization); then the levels of the factor (or the FLCs of two or
more factors) of the most interest are randomized (or split) at the 2nd stage.
In the experiment of Table 14-14, a Pulp Preparation Method is selected at random
from the 3 levels, say that level 2 is selected first, followed by 1 and then 3. So,
the whole-plot random sequence on day one is Method 2, 1, and 3. Next, a large
batch of pulp is prepared using Method 2 first and split into 4 equal-portion
samples. My contention now is that there must be 4 nearly-identical ovens in
order to place the 4 equal-portion samples from Method 2 into the 4 ovens at
random selection. This randomization will average out differences in the 4 Ovens,
if any, over the 3-day span. If there were only one oven and it had to be heated
and reheated to a randomly selected temperature (200, 225, 250, 275), then oven
temperature would constitute the hardest-to-change factor and should become
the whole-plot and not the split-plot. Further, this would be just like Problem 1419 on p. 556 of Montgomery where Oven Temperature is the whole- plot.
With regard to Eric’s question as to why they did not provide samples of all 3
Methods at the same time and insert one sample of each of the 3 methods into
one oven, I would respond that first of all Method levels are not then being
randomized. Secondly, it is harder for a larger oven (containing one sample of
each Method) to maintain uniform temperature throughout the oven; the larger
an oven is, the more difficult it is to have temperature uniformity throughout the
oven.
Thus, the most logical solution is to have 4 ovens available and randomly heat
them to 200, 225, 250, 275 and randomly assign one sample of each method to
the 4 ovens in order to satisfy the requirements of a split-plot design.