In the start-up of a new manufacturing plant, considerable difficulty was experienced with a lime slaking unit. At a meeting to discuss the problem the following seven variables were proposed as being possibly responsible.
Variable
A Lime particle size
B Lime type
C Lime/water ratio
D Stirring rate
E Water used for slaking
F Slaking water temperature
G Additives
+ big hardburned 200 g/1 fast seawater 60°C 1% Ethanol
- small softburned 100 g/1 slow well water 20°C none
In the list above, the plus version corresponds to the usual operating condition and the minus version to a possible change.
A $2^7$ saturated experimental design of resolution III was carried out with the results given below:
Variable Response
Run A B C D E F G
1 - - - - + + + 7.50
2 + - - + - + - 15.05
3 + + - + - - + 15.40
4 + + - - + - - 7.10
5 + - + - - + - 6.60
6 + - + + - - + 15.90
7 - + + - - - + 12.70
8 + + + + + + + 8.70
In each run a sample of the slaked lime produced was titrated with 8 M HCl in an autotitrator operating as a pH stat set to a pH of 7.8. The response measured was the volume of HCl consumed in a standard time -- the larger the value the better the quality of the slaked lime.
A second set of experiments was run, with the contrast signs reversed, yielding the following results:
Run Response
1' 14.00
2' 7.70
3' 8.50
4' 16.00
5' 16.00
6' 8.30
7' 11.00
8' 11.05
Calculate the main effects of the variables, unconfounded with two-factor interactions and comment upon the results.
