Control Chart (Handout).ppt

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.xls


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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

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100

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350

31 32 33 34 35 36 37 38 39 40

Sample

SampleData Upper

Middle

Lower

Data


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Case #2

0

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100

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31 32 33 34 35 36 37 38 39 40

Sample

SampleData Upper

Middle

Lower

Data


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Case #3

0

50

100

150

200

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300

350

31 32 33 34 35 36 37 38 39 40

Sample

SampleData Upper

Middle

Lower

Data


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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.

Control Chart (Handout).ppt

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