566 CHAPTER 14 DESIGN OF EXPERIMENTS WITH SEVERAL FACTORS(a) Estimate the factor effects.
(b) Form a tentative model by examining a normal probabil-
ity plot of the effects.
(c) Is the model in part (b) a reasonable description
of the process? Is lack of fit significant? Use
0.05.
(d) Interpret the results of this experiment.
(e) Analyze the residuals from this experiment.
14-48. Construct a design for the problem in Exercise
14-46. Select the data for the eight runs that would have been
required for this design. Analyze these runs and compare your
conclusions to those obtained in Exercise 14-46 for the full
factorial.
14-49. Construct a design for the problem in Exercise
14-47. Select the data for the eight runs that would have been
required for this design, plus the center points. Analyze these
data and compare your conclusions to those obtained in
Exercise 14-47 for the full factorial.
14-50. Construct a design in 16 runs. What are the
alias relationships in this design?
14-51. Construct a design in eight runs. What are the
alias relationships in this design?
14-52. In a process development study on yield, four fac-
tors were studied, each at two levels: time (A), concentration
(B), pressure (C), and temperature (D). A single replicate
of a 2^4 design was run, and the data are shown in the table
below.(^25) III^2
(^28) IV^4
(^24) IV^1
(^24) IV^1
(a) Plot the effect estimates on a normal probability scale.
Which factors appear to have large effects?
(b) Conduct an analysis of variance using the normal proba-
bility plot in part (a) for guidance in forming an error
term. What are your conclusions?
(c) Analyze the residuals from this experiment. Does your
analysis indicate any potential problems?
(d) Can this design be collapsed into a 2^3 design with two
replicates? If so, sketch the design with the average and
range of yield shown at each point in the cube. Interpret
the results.
14-53. An article in the Journal of Quality Technology
(Vol. 17, 1985, pp. 198–206) describes the use of a replicated
fractional factorial to investigate the effect of five factors on
the free height of leaf springs used in an automotive applica-
tion. The factors are Afurnace temperature, Bheating
time, Ctransfer time, Dhold down time, and E
quench oil temperature. The data are shown in the following
table.
(a) What is the generator for this fraction? Write out the alias
structure.
(b) Analyze the data. What factors influence mean free height?
(c) Calculate the range of free height for each run. Is there any
indication that any of these factors affect variability in free
height?
(d) Analyze the residuals from this experiment and comment
on your findings.
Run Actual Run Yield Factor Levels
Number Order ABCD(lbs) Low () High ()
15 12 A(h) 2.5 3
29 18 B(%) 14 18
38 13 C(psi) 60 80
413 16 D(C) 225 250
53 17
67 15
714 20
81 15
96 10
10 11 25
11 2 13
12 15 24
13 4 19
14 16 21
15 10 17
16 12 23
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