Transcript No Slide Title

The Impact of Variation on Quality: The Xootr Case
Variation is (again) the root cause of all evil
Slide ‹#›
Choosing the Appropriate Control Chart
(MJ II, p. 37)
Attribute (counts)
Defect
Defective
Variable (measurable)
The Lean Six Sigma
Pocket Toolbook, p. 123.
Slide ‹#›
Different types of control charts
Attribute (or count) data
Situation
Number of
defects,
accidents or
flaws
Chart
Control Limits
C
# of accidents/week
# of
breakdowns/week
# of flaws on a
product
U
Lean Six Sigma Pocket Toolbook, p. 132.
Slide ‹#›
source: Brian Joiner, Fourth Generation Management, p. 266-267.
Different types of control charts
Attribute (or count) data
Situation
Fraction of
defectives
Chart
Control Limits
p
fraction of orders not
processed perfectly
on first trial (first pass
yield)
fraction of requests
not processed within
15 minutes
np
Lean Six Sigma Pocket Toolbook, p. 132.
Slide ‹#›
source: Brian Joiner, Fourth Generation Management, p. 266-267.
Different types of control charts
Variables (or measurement ) data
Situation
Variables data,
sets of
measurements
Chart
Control Limits
Xbar and R
Charts
X-”BAR” CHART
X  A2 R
R CHART
See MJ II p. 42 for constants
A2, D3 and D4.
UCL  D4 R
Lean Six Sigma Pocket Toolbook, p. 127.
Slide ‹#›
LCL  D3 R
source: Brian Joiner, Fourth Generation Management, p. 266-267.
Parameters for Creating X-bar Charts
Number of
Observations
in Subgroup
(n)
2
3
4
5
6
7
8
9
10
Factor for Xbar Chart
(A2)
1.88
1.02
0.73
0.58
0.48
0.42
0.37
0.34
0.31
Factor for
Lower
control Limit
in R chart
(D3)
0
0
0
0
0
0.08
0.14
0.18
0.22
Factor to
Factor for
estimate
Upper
Standard
control limit
deviation, (d2)
in R chart
(D4)
1.128
3.27
1.693
2.57
2.059
2.28
2.326
2.11
2.534
2.00
2.704
1.92
2.847
1.86
2.970
1.82
3.078
1.78
Lean Six Sigma Pocket Toolbook, p. 128.
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The X-bar Chart: Application to Call Center
Period
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
x1
x2
1.7
2.7
2.1
1.2
4.4
2.8
3.9
16.5
2.6
1.9
3.9
3.5
29.9
1.9
1.5
3.6
3.5
2.8
2.1
3.7
2.1
3
12.8
2.3
3.8
2.3
2
x3
1.7
2.3
2.7
3.1
2
3.6
2.8
3.6
2.1
4.3
3
8.4
1.9
2.7
2.4
4.3
1.7
5.8
3.2
1.7
2
2.6
2.4
1.6
1.1
1.8
6.7
x4
3.7
1.8
4.5
7.5
3.3
4.5
3.5
2.1
3
1.8
1.7
4.3
7
9
5.1
2.1
5.1
3.1
2.2
3.8
17.1
1.4
2.4
1.8
2.5
1.7
1.8
x5
3.6
3
3.5
6.1
4.5
5.2
3.5
4.2
3.5
2.9
2.1
1.8
6.5
3.7
2.5
5.2
1.8
8
2
1.2
3
1.7
3
5
4.5
11.2
6.3
2.8
2.1
2.9
3
1.4
2.1
3.1
3.3
2.1
2.1
5.1
5.4
2.8
7.9
10.9
1.3
3.2
4.3
1
3.6
3.3
1.8
3.3
1.5
3.6
4.9
1.6
Average
Mean
Range
2.7
2
2.38
1.2
3.14
2.4
4.18
6.3
3.12
3.1
3.64
3.1
3.36
1.1
5.94
14.4
2.66
1.4
2.6
2.5
3.16
3.4
4.68
6.6
9.62
28
5.04
7.1
4.48
9.4
3.3
3.9
3.06
3.4
4.8
5.2
2.1
2.2
2.8
2.6
5.5
15.1
2.1
1.6
4.78
10.4
2.44
3.5
3.1
3.4
4.38
9.5
3.68
5.1
3.81
Slide ‹#›
5.85
• Collect samples over time
• Compute the mean:
X 
x1  x 2  ...  x n
n
• Compute the range:
R  max{x1 , x2 ,...xn }
 min{x1 , x2 ,...xn }
as a proxy for the variance
• Average across all periods
- average mean
- average range
• Normally distributed
Control Charts: The X-bar Chart
• Define control limits
UCL= X +A2 ×R =3.81+0.58*5.85=7.19
LCL= X -A2 ×R =3.81-0.58*5.85=0.41
12
• Constants are taken from a table
10
• Identify assignable causes:
- point over UCL
- point below LCL
- many (6) points on one side of center
8
6
4
2
0
1
3
5
mean
st-dev
7
9
11 13 15 17 19 21 23 25 27
CSR 1
2.95
0.96
• In this case:
- problems in period 13
- new operator was assigned
CSR 2
3.23
2.36
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CSR 3
7.63
7.33
CSR 4
3.08
1.87
CSR 5
4.26
4.41
Attribute Based Control Charts: The p-chart
Period
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
n
300
300
300
300
300
300
300
300
300
300
300
300
300
300
300
300
300
300
300
300
300
300
300
300
300
300
300
300
300
300
defects
18
15
18
6
20
16
16
19
20
16
10
14
21
13
13
13
17
17
21
18
16
14
33
46
10
12
13
18
19
14
p
0.060
0.050
0.060
0.020
0.067
0.053
0.053
0.063
0.067
0.053
0.033
0.047
0.070
0.043
0.043
0.043
0.057
0.057
0.070
0.060
0.053
0.047
0.110
0.153
0.033
0.040
0.043
0.060
0.063
0.047
• Estimate average defect percentage
p =0.052
• Estimate Standard Deviation
sˆ =
p (1  p )
Sam pleSize
=0.013
• Define control limits
UCL= p + 3sˆ =0.091
LCL= p- 3sˆ =0.014
• Divide time into:
- calibration period (capability analysis)
- conformance analysis
Slide ‹#›
Attribute Based Control Charts: The p-chart
0.180
0.160
0.140
0.120
0.100
0.080
0.060
0.040
0.020
0.000
13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Slide ‹#›
Statistical Process Control
Capability
Analysis
Conformance
Analysis
Eliminate
Assignable Cause
Investigate for
Assignable Cause
Capability analysis
• What is the currently "inherent" capability of my process when it is "in control"?
Conformance analysis
• SPC charts identify when control has likely been lost and assignable cause
variation has occurred
Investigate for assignable cause
• Find “Root Cause(s)” of Potential Loss of Statistical Control
Eliminate or replicate assignable cause
• Need Corrective Action To Move Forward
Slide ‹#›
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
1
16.09
15.95
16.07
16.13
16.16
2
16.16
16.00
16.07
16.15
16.11
Sample
3
16.08
15.90
16.08
16.19
16.40
4
16.02
16.17
15.89
16.13
16.14
5
16.11
16.01
16.28
16.19
15.86
Average
16.09
16.01
16.08
16.16
16.13
Range
0.14
0.27
0.39
0.06
0.54
If the specification limits are USL = 16.539 and LSL = 15.829 is the
process capable?
Slide ‹#›
Consider a data entry
operation that makes
numerous entries daily.
On each of 24
consecutive days
subgroups of 200 entries
are inspected. Develop a
p control chart for this
process.
Gitlow, Openheim, Openheim & Levine, Quality
Management, 3ed.
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Revised Data
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