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8/21/2019 Control Chart (Handout).ppt
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Process Control Charts
Process Control is a technique for inferring that anunplanned change has taken place in a processmeasured by a process variableX.
Example: Xis the exact weight of a bag of cement
intended to weigh 200 pounds.
Any process has a certain amount of naturalvariability. But how can we tell if the processsvariability has gone out of control?
Example: An automated process whose intent is tofill a bag with 200 pounds of cement.
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Alternative Meanings forthe Process VariableX
The salt content, thickness, or crispness ofa bag of potato chips.
The number of chocolate chips in acontainer of chocolate-chip ice cream.
The diameter of a bearing, or the center ofa gear.
The waiting time at a fast-food restaurantor at an airport check-in counter.
The internal temperature of a rare steakwhen it leaves a restaurants kitchen.
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SamplingOver some period of time, take Nsamples with eachsample having nobservations.
Example: During each of N=10 consecutive hours,remove n=4 bags of cements from the filling process andweigh them.
OBSERVATIONS
SAMPLE 1 199.98 200.37 200.94 200.80
SAMPLE 2 200.42 201.04 199.91 199.80
SAMPLE 3 199.59 200.08 199.04 198.47
SAMPLE 4 200.44 201.34 199.39 200.09
SAMPLE 5 199.80 199.37 200.41 196.63
SAMPLE 6 199.68 198.52 201.73 198.99
SAMPLE 7 199.83 201.68 198.53 200.33
SAMPLE 8 197.65 199.67 200.04 199.52
SAMPLE 9 199.11 200.75 200.86 199.76
SAMPLE 10 199.65 198.98 201.33 199.65
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Two Ways a Process Can beOut-of-Control
Both of the processes below are out-of-control.
But in different ways! Can you see the difference?
SAMPLE 1 20 10 30
SAMPLE 2 40 30 20
SAMPLE 3 40 50 30
SAMPLE 4 50 40 60
OBSERVATIONS
SAMPLE 1 20 10 30
SAMPLE 2 31 20 9
SAMPLE 3 8 32 20
SAMPLE 4 33 20 7
OBSERVATIONS
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Two Ways to be Out-of-Control (continued)
SAMPLE 1 20 10 30
SAMPLE 2 40 30 20
SAMPLE 3 40 50 30
SAMPLE 4 50 40 60
OBSERVATIONS
SAMPLE 1 20 10 30
SAMPLE 2 31 20 9
SAMPLE 3 8 32 20
SAMPLE 4 33 20 7
OBSERVATIONS
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Establishing theControl Charts UCL & LCL
Go to Excel Workbook
http://localhost/var/www/apps/conversion/Excel%20Files/Control%20Chart/Template.xlshttp://localhost/var/www/apps/conversion/Excel%20Files/Control%20Chart/Template.xls8/21/2019 Control Chart (Handout).ppt
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Establishing theControl Charts UCL & LCL (continued)
X-bar Control Chart
180
190
200
210
220
1 2 3 4 5 6 7 8 9 10
Sample
SampleMean
UCL
X-bar-bar
LCL
Range Control Chart
0
10
20
30
40
1 2 3 4 5 6 7 8 9 10
Sample
SampleRange
UCL
R-bar
LCL
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The Mean is out-of-control!
Range Control Chart
0
10
20
30
40
31 32 33 34 35 36 37 38 39 40
Sample
SampleRange
UCL
R-bar
LCL
Range
X-bar Control Chart
180
185
190
195
200
205
210
215
31 32 33 34 35 36 37 38 39 40
Sample
SampleMean UCL
X-bar-bar
LCL
Sample Mean
Sample X-bar Range
31 203 198 191 212 201.000 21
32 205 188 207 197 199.250 19
33 199 199 205 197 200.000 8
34 211 200 208 202 205.250 11
35 197 194 203 199 198.250 9
36 187 200 193 205 196.250 18
37 195 214 216 193 204.500 23
38 218 207 223 205 213.250 18
39 199 193 208 195 198.750 15
40 208 201 201 195 201.250 13
Sample Data
Out-of-control
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The Range is out-of-control!
X-bar Control Chart
180
185
190
195
200
205
210
215
31 32 33 34 35 36 37 38 39 40
Sample
SampleMean UCL
X-bar-bar
LCL
Sample Mean
Range Control Chart
0
10
20
30
40
31 32 33 34 35 36 37 38 39 40
Sample
SampleRange
UCL
R-bar
LCL
Range
Sample X-bar Range
31 190 199 198 199 196.500 9
32 224 207 195 192 204.500 32
33 186 199 199 209 198.250 23
34 211 204 194 202 202.750 17
35 217 200 188 200 201.250 29
36 204 202 184 195 196.250 20
37 193 200 201 205 199.750 12
38 211 208 212 173 201.000 39
39 205 205 202 211 205.750 9
40 188 198 178 207 192.750 29
Sample Data
Out-of-control
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Patterns to InvestigateCase #1
Why might this process be out-of-control?
Case #1
0
50
100
150
200
250
300
350
31 32 33 34 35 36 37 38 39 40
Sample
SampleData Upper
Middle
Lower
Data
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Patterns to InvestigateCase #2
Why might this process be out-of-control?
Case #2
0
50
100
150
200
250
300
350
31 32 33 34 35 36 37 38 39 40
Sample
SampleData Upper
Middle
Lower
Data
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Patterns to InvestigateCase #3
Why might this process be out-of-control?
Case #3
0
50
100
150
200
250
300
350
31 32 33 34 35 36 37 38 39 40
Sample
SampleData Upper
Middle
Lower
Data
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Patterns to InvestigateCase #4
Why might this process be out-of-control?
Case #4
0
50
100
150
200
250
300
350
31 32 33 34 35 36 37 38 39 40
Sample
SampleData Upper
Middle
Lower
Data
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The Process Control Cycle
Initialization. Take an initial set of Nsamples with nobservations, and use these to compute the initial lower andupper control limits.
Step 1. Continue with periodic samples until the process goesout-of-control. Look for an assignable cause.
Step 3. After a process improvement, recalibrate the lowerand upper control limits by taking another set of Nsamples
with nobservations. Return to Step 1.
Step 2. If possible, improve the process in a manner thatdecreases the chance that the same assignable cause will
reoccur.
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Another Type of Control Chart
We have discussed control charts in the context of a processwhose performance is measured by a continuous variableX.
For some processes, performance is measured by an binaryattribute an attribute that is either present or not present.
Examples:
A product is either defective or non-defective.
A invoice either contains an error or is error-free.A customer is either satisfied or unsatisfied.
To control a process measured by an binary attribute, youneed to use another type of control chart known as ap-chart.