564 CHAPTER 14 DESIGN OF EXPERIMENTS WITH SEVERAL FACTORS14-34. Consider the 2^6 ^2 design in Table 14-28. Suppose
that after analyzing the original data, we find that factors C
and Ecan be dropped. What type of 2kdesign is left in the re-
maining variables?
14-35. Consider the 2^6 ^2 design in Table 14-28. Suppose
that after the original data analysis, we find that factors Dand
Fcan be dropped. What type of 2kdesign is left in the remain-
ing variables? Compare the results with Exercise 14-34. Can
you explain why the answers are different?
14-36. Suppose that in Exercise 14-22 it was possible to
run only a ^12 fraction of the 2^4 design. Construct the design and
use only the data from the eight runs you have generated to
perform the analysis.
14-37. Suppose that in Exercise 14-16 only a^1 ⁄ 4 fraction
of the 2^5 design could be run. Construct the design and analyze
the data that are obtained by selecting only the response for
the eight runs in your design.
14-38. Construct the 2IV^8 ^4 design recommended in Table
13-29. What are the aliases of the main effects and two-factor
interactions?
14-39. Construct a 2III^6 ^3 fractional factorial design. Write
down the aliases, assuming that only main effects and two-
factor interactions are of interest.
14-40. Consider the problem in Exercise 14-19. Suppose
that only half of the 32 runs could be made.
(a) Choose the half that you think should be run.
(b) Write out the alias relationships for your design.
(c) Estimate the factor effects.
(d) Plot the effect estimates on normal probability paper and
interpret the results.
(e) Set up an analysis of variance for the factors identified as
potentially interesting from the normal probability plot in
part (d).
(f) Analyze the residuals from the model.
(g) Provide a practical interpretation of the results.14-10 RESPONSE SURFACE METHODS
AND DESIGNS (CD ONLY)Supplemental Exercises14-41. An article in Process Engineering(No. 71, 1992, pp.
46 – 47) presents a two-factor factorial experiment used toinvestigate the effect of pH and catalyst concentration on prod-
uct viscosity (cSt). The data are as follows:Catalyst Concentration
2.5 2.7
pH 5.6 192, 199, 189, 198 178, 186, 179, 188
5.9 185, 193, 185, 192 197, 196, 204, 204Time (minutes)
Gear Type 90 120
20-tooth 0.0265 0.0560
0.0340 0.0650
24-tooth 0.0430 0.0720
0.0510 0.0880
28-tooth 0.0405 0.0620
0.0575 0.0825Salt
Level Untreated MgCl 2 NaCl CaCO 3 CaCl 2 Na 2 CO 3
1 812 752 739 733 725 751
827 728 731 728 727 761
876 764 726 720 719 755
2 945 794 741 786 756 910
881 760 744 771 781 854
919 757 727 779 814 848(a) Test for main effects and interactions using 0.05.
What are your conclusions?
(b) Graph the interaction and discuss the information provided
by this plot.
(c) Analyze the residuals from this experiment.
14-42. Heat treating of metal parts is a widely used manu-
facturing process. An article in the Journal of Metals(Vol. 41,
1989) describes an experiment to investigate flatness distor-
tion from heat treating for three types of gears and two heat-
treating times. The data are as follows:(a) Is there any evidence that flatness distortion is different
for the different gear types? Is there any indication that
heat treating time affects the flatness distortion? Do these
factors interact? Use 0.05.
(b) Construct graphs of the factor effects that aid in drawing
conclusions from this experiment.
(c) Analyze the residuals from this experiment. Comment on
the validity of the underlying assumptions.
14-43. An article in the Textile Research Institute Journal
(Vol. 54, 1984, pp. 171–179) reported the results of an exper-
iment that studied the effects of treating fabric with selected
inorganic salts on the flammability of the material. Two appli-
cation levels of each salt were used, and a vertical burn test
was used on each sample. (This finds the temperature at which
each sample ignites.) The burn test data follow.c 14 .qxd 5/9/02 7:55 PM Page 564 RK UL 6 RK UL 6:Desktop Folder:TEMP WORK:MONTGOMERY:REVISES UPLO D CH112 FIN L: