14-10 RESPONSE SURFACE METHODS AND DESIGNS (CD ONLY) 563This 2III^7 ^4 design is called a saturated fractional factorial,because all the available
degrees of freedom are used to estimate main effects. It is possible to combine sequences of
these resolution III fractional factorials to separate the main effects from the two-factor
interactions. The procedure is illustrated in Montgomery (2001) and in Box, Hunter, and
Hunter (1978).14-31. R. D. Snee (“Experimenting with a Large Number of
Variables,” in Experiments in Industry: Design, Analysis and
Interpretation of Results,by R. D. Snee, L. D. Hare, and J. B.
Trout, eds., ASQC, 1985) describes an experiment in which
a2^5 ^1 design with IABCDEwas used to investigate the
effects of five factors on the color of a chemical product.
The factors are Asolvent/reactant, Bcatalyst/reactant,
Ctemperature, Dreactant purity, and Ereactant pH.
The results obtained are as follows:(a) Prepare a normal probability plot of the effects. Which
factors are active?
(b) Calculate the residuals. Construct a normal probability
plot of the residuals and plot the residuals versus the fitted
values. Comment on the plots.
(c) If any factors are negligible, collapse the 2^5 ^1 design into
a full factorial in the active factors. Comment on the re-
sulting design, and interpret the results.
14-32. Montgomery (2001) describes a 2^4 ^1 fractional fac-
torial design used to study four factors in a chemical process.
The factors are Atemperature, Bpressure, Cconcen-
tration, and Dstirring rate, and the response is filtration
rate. The design and the data are as follows:e0.63 d6.79
a 2.51 ade6.47
b2.68 bde3.45
abe 1.66 abd5.68
c 2.06 cde5.22
ace 1.22 acd4.38
bce2.09 bcd4.30
abc 1.93 abcde 4.05EXERCISES FOR SECTION 14-9
(a) Write down the alias relationships.
(b) Estimate the factor effects. Which factor effects appear
large?
(c) Project this design into a full factorial in the three appar-
ently important factors and provide a practical interpreta-
tion of the results.
14-33. An article in Industrial and Engineering Chemistry
(“More on Planning Experiments to Increase Research
Efficiency,” 1970, pp. 60–65) uses a 2^5 ^2 design to investigate
the effect on process yield of Acondensation temperature,
Bamount of material 1, Csolvent volume, Dcon-
densation time, and Eamount of material 2. The results ob-
tained are as follows:(a) Verify that the design generators used were IACEand
IBDE.
(b) Write down the complete defining relation and the aliases
from the design.
(c) Estimate the main effects.
(d) Prepare an analysis of variance table. Verify that the AB
and ADinteractions are available to use as error.
(e) Plot the residuals versus the fitted values. Also construct a
normal probability plot of the residuals. Comment on the
results.ae23.2 cd23.8
ab15.5 ace23.4
ad16.9 bde16.8
bc16.2 abcde18.1Treatment Filtration
Run ABCDABC Combination Rate
1 45
2 ad 100
3 bd 45
4 ab 65
5 cd 75
6 ac 60
7 bc 80
8 abcd 96112c 14 .qxd 5/9/02 7:54 PM Page 563 RK UL 6 RK UL 6:Desktop Folder:TEMP WORK:MONTGOMERY:REVISES UPLO D CH112 FIN L: