Applied Statistics and Probability for Engineers

558 CHAPTER 14 DESIGN OF EXPERIMENTS WITH SEVERAL FACTORS

insensitive to temperature if the screw speed is at the low level but sensitive to temperature

if the screw speed is at the high level. With the screw speed at a low level, the process

should produce an average shrinkage of around 10% regardless of the temperature level

chosen.

Based on this initial analysis, the team decides to set both the mold temperature and the

screw speed at the low level. This set of conditions should reduce the mean shrinkage of parts

to around 10%. However, the variability in shrinkage from part to part is still a potential prob-

lem. In effect, the mean shrinkage can be adequately reduced by the above modifications;

however, the part-to-part variability in shrinkage over a production run could still cause prob-

lems in assembly. One way to address this issue is to see if any of the process factors affect the

variability in parts shrinkage.

Figure 14-35 presents the normal probability plot of the residuals. This plot appears

satisfactory. The plots of residuals versus each factor were then constructed. One of these

plots, that for residuals versus factor C(holding time), is shown in Fig. 14-36. The plot

reveals much less scatter in the residuals at the low holding time than at the high holding

time. These residuals were obtained in the usual way from a model for predicted

shrinkage

where x 1 , x 2 , and x 1 x 2 are coded variables that correspond to the factors Aand Band the AB

interaction. The residuals are then

The regression model used to produce the residuals essentially removes the location ef-

fects of A, B, and ABfrom the data; the residuals therefore contain information about

unexplained variability. Figure 14-36 indicates that there is a pattern in the variability and

eyyˆ

27.31256.9375x 1 17.8125x 2 5.9375x 1 x 2

yˆˆ 0 ˆ 1 x 1 ˆ 2 x 2 ˆ 12 x 1 x 2

• 6 – 3036
  Residual

Normal probability

1

5

10

20

30

50

70

80

90

95

99

Low

• 4

High

• 2

0

2

4

6

Holding time (C)

Residuals

• 6

Figure 14-35 Normal probability plot of resid-

uals for Example 14-8.

Figure 14-36 Residuals versus holding time

(C) for Example 14-8.

c 14 .qxd 5/9/02 7:54 PM Page 558 RK UL 6 RK UL 6:Desktop Folder:TEMP WORK:MONTGOMERY:REVISES UPLO D CH112 FIN L: