Applied Statistics and Probability for Engineers

14-9 FRACTIONAL REPLICATION OF THE 2kDESIGN 557

pressure (F)—each at two levels, with the objective of learning how each factor affects shrink-

age and obtaining preliminary information about how the factors interact.

The team decides to use a 16-run two-level fractional factorial design for these six factors.

The design is constructed by writing down a 2^4 as the basic design in the factors A,B,C, and D

and then setting E ABCand F BCDas discussed above. Table 14-28 shows the design, along

with the observed shrinkage (10) for the test part produced at each of the 16 runs in the design.

A normal probability plot of the effect estimates from this experiment is shown in Fig. 14-33.

The only large effects are A(mold temperature), B(screw speed), and the ABinteraction.

In light of the alias relationship in Table 14-27, it seems reasonable to tentatively adopt

these conclusions. The plot of the ABinteraction in Fig. 14-34 shows that the process is

Table 14-28 A Design for the Injection-Molding Experiment in Example 14-8

Observed

Shrinkage

Run ABCDE ABC F BCD (10)

1  6

2  10

3  32

4  60

5  4

6  15

7  26

8  60

9  8

10  12

11  34

12  60

13  16

14  5

15  37

16  52

(^2) IV^6 ^2
Figure 14-33 Normal probability plot of effects
for Example 14-8.

• 5

1

0 5 10 15 20 25 30 35 40

5

10

20

30

50

60

80

90

95

99

AB

A

B

Normal probability

Effect

Low

60

4

High

Shrinkage (

× 10)

Mold temperature, A

B–

B+

B+

B–

Figure 14-34 Plot of AB(mold

temperature–screw speed) interaction

for Example 14-8.

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