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29.4 Fly Ash. Verify that calculating the main effects of factors 1 and 2 in the case study from the
collapsed (apparently replicated) design in Figure 29.3 gives the same results reported in
Table 29.5.
29.5 Oxygen Transfer. Reaeration experiments in a laboratory flume were studied using a screening
7–4
2 design and its “fold-over.” A fold-over design simply does a second set of eight experi-
ments with all the signs switched (+ to −, and − to +). Main effects are estimated free of two-
factor interactions, and two-factor interactions are confounded in groups of three. The factors
studied were depth (3 and 6 in.), velocity (1 and 1.5 fps), roughness (smooth and rough),
2
temperature (20 and 25°C), surface area (4.6 and 9.2 ft ), straightening grid (not used, used),
−1
and division vane (area, flow). The response is oxygen transfer coefficient, k 2 , (day ). The
experimental design and results are given below. Evaluate the main and interaction effects of
these factors. Which are most important in affecting the oxygen transfer coefficient?

Run Depth Vel. Roughness Temp. Area Grid Vane k 2
1 − − − − + + + 15.0
2 + − − + + − − 10.2
3 − + − + − − + 28.9
4 + + − − − + − 12.1
5 − − + + − + − 24.4
6 + − + − − − + 9.6
7 − + + − + − − 28.9
8 + + + + + + + 11.4
9 + + + + − − − 18.0
10 − + + − − + + 34.1
11 + − + − + + − 8.3
12 − − + + + − + 21.6
13 + + − − + − + 13.4
14 − + − + + + − 23.7
15 + − − + − + + 10.1
16 − − − − − − − 18.1
7−4
Note: The design identity for the 2 design is I == == 1234 == == 235 == == 126 == == 137.
The design identity for the fold-over design is I == == 1234 == == −− −−235 == == −− −−126 == == −− −−137.

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