Transcript No Slide Title
Choosing the Appropriate Control Chart
(MJ II, p. 37) Attribute (counts) Variable (measurable) Defect Defective
The Lean Six Sigma Pocket Toolbook, p. 123.
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Different types of control charts
Variables (or measurement ) data Situation Chart Control Limits
Variables data, sets of measurements Xbar and R Charts
X-”BAR” CHART
X
A
2
R
See MJ II p. 42 for constants A 2 , D 3 and D 4 .
R CHART
UCL
D
4
R LCL
D
3
R
Lean Six Sigma Pocket Toolbook, p. 127.
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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 X bar Chart (A
2
)
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 (D
3
)
0 0 0 0 0 0.08 0.14 0.18 0.22
Lean Six Sigma Pocket Toolbook, p. 128.
Factor for Upper control limit in R chart (D
4
)
3.27 2.57 2.28 2.11 2.00 1.92 1.86 1.82 1.78
Factor to estimate Standard deviation, (d
2
)
1.128 1.693 2.059 2.326 2.534 2.704 2.847 2.970 3.078
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X Bar Chart
86 84 82 80 78 76 1 3 5 7 9 11 13 15 17 19 Day
Average X bar = 82.5 psi
UCL LCL
Standard Deviation of X bar = 1.6 psi Control Limits = Avg X bar + 3 Std of X bar = 82.5 + (3)(1.6) = [77.7, 87.3] Process is “
In Control
” (i.e., the mean is stable)
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Range (R) Chart
20 15 10 5 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Day
Average Range R = 10.1 psi Standard Deviation of Range = 3.5 psi Control Limits: 10.1 + (3)(3.5) = [0, 20.6] Process Is “
In Control
” (i.e., variation is stable)
UCL LCL
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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?
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Different types of control charts
Attribute (or count) data Situation Chart Control Limits
Fraction of defectives
fraction of orders not processed perfectly on first trial (first pass yield) p fraction of requests not processed within 15 minutes np
Lean Six Sigma Pocket Toolbook, p. 132.
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source: Brian Joiner, Fourth Generation Management, p. 266-267.
Attribute Based Control Charts: The p-chart
Period n defects p
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 24 25 26 27 28 29 30 1 8 9 10 11 12 2 3 4 5 6 7 19 20 21 22 23 13 14 15 16 17 18 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
46 10 12 13 18 19 14 18 19 20 16 10 14 15 18 6 20 16 16 21 18 16 14 33 21 13 13 13 17 17 • Estimate average defect percentage
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s ˆ =
p
=0.052
• Estimate Standard Deviation
p
( 1
p
)
Sample Size
• Define control limits
p
s ˆ
p
s ˆ =0.013
=0.091
=0.014
• Divide time into: - calibration period (capability analysis) - conformance analysis
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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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Control, Capability and Design: Review
Every process displays variation in performance: normal or abnormal Do not tamper with a process that is “in control” with normal variation Correct an “out of control” process with abnormal variation Control charts monitor process to identify abnormal variation Control charts may cause false alarms (or missed signals) by mistaking normal (abnormal) variation for abnormal (normal) variation Local control yields early detection and correction of abnormal variation Process “in control” indicates only its internal stability Process capability is its ability to meet external customer needs Improving process capability involves (a) changing the mean in the short run, and (b) reducing normal variability in the long run, requiring investment Robust, simple, standard, mistake - proof design improves process capability Joint, early involvement in design by all improves product quality, speed, cost
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Capability and Design: Review
Process capability measures its precision in meeting processing requirements Improving capability involves reducing variation and its impact on product quality Simplicity, standardization, and mistake - proofing improve process capability Joint design and early involvement minimizes quality problems, delays, cost
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