542 CHAPTER 14 DESIGN OF EXPERIMENTS WITH SEVERAL FACTORS14-15. Consider the experiment in Exercise 14-14.
Determine an appropriate model and plot the residuals against
the levels of factors A, B, C, and D. Also construct a normal
probability plot of the residuals. Comment on these plots.
14-16. The data shown here represent a single replicate of a
25 design that is used in an experiment to study the compres-
sive strength of concrete. The factors are mix (A), time (B),
laboratory (C), temperature (D), and drying time (E).(a) Estimate the factor effects.
(b) Which effects appear important? Use a normal probability
plot.
(c) If it is desirable to maximize the strength, in which direc-
tion would you adjust the process variables?
(d) Analyze the residuals from this experiment.
14-17. An article in the IEEE Transactions on Semiconduc-
tor Manufacturing(Vol. 5, no. 3, 1992, pp. 214–222) de-
scribes an experiment to investigate the surface charge on a
silicon wafer. The factors thought to influence induced surface
charge are cleaning method (spin rinse dry or SRD and spin
dry or SD) and the position on the wafer where the charge was
measured. The surface charge ( 1011 q/cm^3 ) response data are
as shown.112 700 e 800
a 900 ae 1200
b 3400 be 3500
ab 5500 abe 6200
c 600 ce 600
ac 1000 ace 1200
bc 3000 bce 3006
abc 5300 abce 5500
d 1000 de 1900
ad 1100 ade 1500
bd 3000 bde 4000
abd 6100 abde 6500
cd 800 cde 1500
acd 1100 acde 2000
bcd 3300 bcde 3400
abcd 6000 abcde 680014-18. An experiment described by M. G. Natrella in the
National Bureau of Standards Handbook of Experimental
Statistics(No. 91, 1963) involves flame testing fabrics after
applying fire-retardant treatments. The four factors considered
are type of fabric (A), type of fire-retardant treatment (B),
laundering condition (C—the low level is no laundering, the
high level is after one laundering), and method of conducting
the flame test (D). All factors are run at two levels, and the re-
sponse variable is the inches of fabric burned on a standard
size test sample. The data are:(a) Estimate the effects and prepare a normal plot of the
effects.
(b) Construct an analysis of variance table based on the model
tentatively identified in part (a).
(c) Construct a normal probability plot of the residuals and
comment on the results.
14-19. An experiment was run in a semiconductor fabrica-
tion plant in an effort to increase yield. Five factors, each at
two levels, were studied. The factors (and levels) were
Aaperture setting (small, large), Bexposure time (20%
below nominal, 20% above nominal), Cdevelopment time
(30 and 45 seconds), Dmask dimension (small, large), and
Eetch time (14.5 and 15.5 minutes). The following un-
replicated 2^5 design was run:(a) Construct a normal probability plot of the effect estimates.
Which effects appear to be large?112 7 e 8
a 9 ae 12
b 34 be 35
ab 55 abe 52
c 16 ce 15
ac 20 ace 22
bc 40 bce 45
abc 60 abce 65
d 8 de 6
ad 10 ade 10
bd 32 bde 30
abd 50 abde 53
cd 18 cde 15
acd 21 acde 20
bcd 44 bcde 41
abcd 61 abcde 63112 42 d 40
a 31 ad 30
b 45 bd 50
ab 29 abd 25
c 39 cd 40
ac 28 acd 25
bc 46 bcd 50
abc 32 abcd 23Test Position
LR
1.66 1.84
SD 1.90 1.84
1.92 1.62
4.21 7.58
SRD 1.35 2.20
2.08 5.36(a) Estimate the factor effects.
(b) Which factors appear important? Use 0.05.
(c) Analyze the residuals from this experiment.Cleaning
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