Applied Statistics and Probability for Engineers

618 CHAPTER 16 STATISTICAL QUALITY CONTROL

Some individuals have suggested that limits narrower than 3-sigma be used on the chart

for individuals to enhance its ability to detect small process shifts. This is a dangerous sug-

gestion, for narrower limits will dramatically increase false alarms such that the charts may be

ignored and become useless. If you are interested in detecting small shifts, use the cumulative

sum or exponentially weighted moving-average control chart referred to on the previous page.

0

92

95

98

101

104

107

4 8 12 16 20

UCL = 105.99

LCL = 92.21

UCL = 8.46

Individuals

0

0

2

4

6

8

10

4 8 12 16 20

Moving range (2)

Subgroup

Subgroup

LCL =

0.000

x =

99.10

r =

2.59

Figure 16-11

Control charts for

individuals and the

moving range (from

Minitab) for the

chemical process

concentration data.

EXERCISES FOR SECTION 16-6

Observation Hardness Observation Hardness

151 1151

252 1257

354 1358

455 1450

555 1553

651 1652

752 1754

850 1850

951 1956

10 56 20 53

16-9. Twenty successive hardness measurements are made

on a metal alloy, and the data are shown in the following table.

(a) Using all the data, compute trial control limits for indi-

vidual observations and moving-range charts. Construct

the chart and plot the data. Determine whether the

process is in statistical control. If not, assume assignable

causes can be found to eliminate these samples and re-

vise the control limits.

(b) Estimate the process mean and standard deviation for the

in-control process.

16-10. In a semiconductor manufacturing process CVD

metal thickness was measured on 30 wafers obtained over ap-

proximately two weeks. Data are shown in the following table.

(a) Using all the data, compute trial control limits for indi-

vidual observations and moving-range charts. Construct

the chart and plot the data. Determine whether the

process is in statistical control. If not, assume assignable

causes can be found to eliminate these samples and re-

vise the control limits.

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