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−1 −1 +1 +1 64
+1 −1 +1 −1 87
−1 +1 +1 −1 81
+1 +1 +1 +1 68
Note: Defining relation: I = 1234.
Source: Cantor, J. et al. (1999). Ind. Wastewater, Nov./Dec., pp. 18–22.
28.2 Corrosion. A study of the effect of construction metal corrosion under simulated acid fog/rain
conditions used factorial experimental designs with pH, salinity, temperature, and exposure
4−1
time as variables. The 2 experiment was performed on galvanized steel and the response
was corrosion rate. Each run was replicated n = 17 times. Estimate the main effects of the four
factors and the two-factor interactions. Note that the design identity is I == == 1234, so the two-
factor interactions are confounded with other two-factor interactions.

Salinity Temp. Time Avg. Corrosion St. Dev.
Run pH (%NaCl) (°° °°C) (hr) Rate (µµ µµ m/yr) (µµ µµ m/yr)
1 2.5 1.0 35 48 501 65
2 3.5 1.0 35 120 330 60
3 2.5 6.0 35 120 561 67
4 3.5 6.0 35 48 666 95
5 2.5 1.0 45 120 218 85
6 3.5 1.0 45 48 247 57
7 2.5 6.0 45 48 710 102
8 3.5 6.0 45 120 438 51
Source: Fang, H. H. P. et al. (1990). Water, Air, and Soil Poll., 53, 315–325.
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28.3 Fly Ash Mixture. The table below describes a 2 experiment in 16 runs to investigate five
factors: (1) type of fly ash, (2) percentage fly ash in the mixture, (3) test specimens put
through a wet/dry curing cycle, (4) test specimens put through a freeze/thaw curing cycle,
and (5) percentage of bentonite in the mixture. High permeability is desirable. What combi-
nation of factors promotes this? Quantify the effect of the five factors. Evaluate and explain
any interactions between factors.

Type of Fly Ash Wet/Dry Freeze/Thaw Bentonite
Run Fly Ash (%) Cycle Cycle (%) Permeability
1 A 50 N N 10 1000
2 B 50 N N 0 160
3 A 100 N N 0 1450
4 B 100 N N 10 77
5 A 50 Y N 0 1400
6 B 50 Y N 10 550
7 A 100 Y N 10 320
8 B 100 Y N 0 22
9 A 50 N Y 0 1400
10 B 50 N Y 10 390
11 A 100 N Y 10 580
12 B 100 N Y 0 8
13 A 50 Y Y 10 2800
14 B 50 Y Y 0 160
15 A 100 Y Y 0 710
16 B 100 Y Y 10 19

4
28.4 Metal Inhibition. Divide the 2 factorial experiment in Exercise 27.5 into two half-fractions.
Calculate the main effects and interactions of each half-fraction and compare them.
© 2002 By CRC Press LLC