Control Chart Samole
QUAN 6610
Tool: Control Chart 1
Slide 1Slide 1
Choosing the Appropriate Control Chart
(MJ II, p. 37)
Attribute (counts Variable (measurable)
or classification)
Defect Defective
(count) (classification)
The Lean Six Sigma
Pocket Toolbook, p. 123.
Slide 2Slide 2
Different types of control charts
Attribute (or count) data
Situation Chart Control Limits
Number of
defects,
accidents or
flaws
# of accidents/week
# of
breakdowns/week
# of flaws on a
product
C
U
source: Brian Joiner, Fourth Generation Management, p. 266-267.
Lean Six Sigma Pocket Toolbook, p. 132.
Slide 3Slide 3
Different types of control charts
Attribute (or classification) data
Situation Chart Control Limits
Fraction of
defectives
fraction of orders not
processed perfectly
on first trial (first pass
yield)
fraction of requests
not processed within
15 minutes
p
np
source: Brian Joiner, Fourth Generation Management, p. 266-267.
Lean Six Sigma Pocket Toolbook, p. 132.
Slide 4Slide 4
Different types of control charts
Variables (or measurement ) data
Situation Chart Control Limits
Variables data,
sets of
measurements
Xbar and R
Charts
source: Brian Joiner, Fourth Generation Management, p. 266-267.
RAX
2
±
RDLCL
RDUCL
3
4
=
=
X-”BAR” CHART
R CHART
See MJ II p. 42 for constants
A
2
, D
3
and D
4
.
Lean Six Sigma Pocket Toolbook, p. 127.
Slide 5Slide 5
Number of
Observations
in Subgroup
(
n
)
Factor for X-
bar Chart
(
A
2
)
Factor for
Lower
control Limit
in R chart
(
D
3
)
Factor for
Upper
control limit
in R chart
(
D
4
)
Factor to
estimate
Standard
deviation, (
d
2
)
2 1.88 0 3.27 1.128
3 1.02 0 2.57 1.693
4 0.73 0 2.28 2.059
5 0.58 0 2.11 2.326
6 0.48 0 2.00 2.534
7 0.42 0.08 1.92 2.704
8 0.37 0.14 1.86 2.847
9 0.34 0.18 1.82 2.970
10 0.31 0.22 1.78 3.078
Parameters for Creating X-bar Charts
Lean Six Sigma Pocket Toolbook, p. 128.
Slide 6Slide 6
Exercise An automatic filling machine is used to fill 16
ounce cans of a certain product. Samples of size 5 are
taken from the assembly line each hour and measured.
The results of the first 25 subgroups are shown in the
attached file with selected rows shown below.
Does the process appear to be in statistical control?
Source: Shirland, Statistical Quality Control, problem 5.2.
Filling Weights
subgroup 1 2 3 4 5 Average
Range
1 16.09 16.16 16.08 16.02 16.11 16.09 0.14
2 15.95 16.00 15.90 16.17 16.01 16.01 0.27
3 16.07 16.07 16.08 15.89 16.28 16.08 0.39
4 16.13 16.15 16.19 16.13 16.19 16.16 0.06
5 16.16 16.11 16.40 16.14 15.86 16.13 0.54
Sample
If the specification limits are USL = 16.539 and LSL = 15.829 is the
process capable?
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