Control Chart (Handout)

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Process Control Charts

Process Control is a technique for inferring that an unplanned change has taken place in a process measured by a process variable X.Example: X is the exact weight of a bag of cement intended to weigh 200 pounds.

Any process has a certain amount of natural variability. But how can we tell if the process’s variability has gone “out of control”?Example: An automated process whose intent is to fill a bag with 200 pounds of cement.

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Alternative Meanings forthe Process Variable X

The salt content, thickness, or crispness of a bag of potato chips.

The number of chocolate chips in a container of chocolate-chip ice cream.

The diameter of a bearing, or the center of a gear.

The waiting time at a fast-food restaurant or at an airport check-in counter.

The internal temperature of a “rare” steak when it leaves a restaurant’s kitchen.

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SamplingOver some period of time, take N samples with each sample having n observations.Example: During each of N=10 consecutive hours, remove n=4 bags of cements from the filling process and weigh them.

OBSERVATIONSSAMPLE 1 199.98 200.37 200.94 200.80SAMPLE 2 200.42 201.04 199.91 199.80SAMPLE 3 199.59 200.08 199.04 198.47SAMPLE 4 200.44 201.34 199.39 200.09SAMPLE 5 199.80 199.37 200.41 196.63SAMPLE 6 199.68 198.52 201.73 198.99SAMPLE 7 199.83 201.68 198.53 200.33SAMPLE 8 197.65 199.67 200.04 199.52SAMPLE 9 199.11 200.75 200.86 199.76SAMPLE 10 199.65 198.98 201.33 199.65

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Two Ways a Process Can be Out-of-Control

Both of the processes below are out-of-control.But in different ways! Can you see the difference?

SAMPLE 1 20 10 30SAMPLE 2 40 30 20SAMPLE 3 40 50 30SAMPLE 4 50 40 60

OBSERVATIONSSAMPLE 1 20 10 30SAMPLE 2 31 20 9SAMPLE 3 8 32 20SAMPLE 4 33 20 7

OBSERVATIONS

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Two Ways to be Out-of-Control (continued)

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Establishing theControl Chart’s UCL & LCL

Go to Excel Workbook

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Establishing theControl Chart’s UCL & LCL (continued)

X-bar Control Chart

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Range Control Chart

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The Mean is out-of-control!

Range Control Chart

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X-bar Control Chart

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Sample Mean

Sample X-bar Range31 203 198 191 212 201.000 2132 205 188 207 197 199.250 1933 199 199 205 197 200.000 834 211 200 208 202 205.250 1135 197 194 203 199 198.250 936 187 200 193 205 196.250 1837 195 214 216 193 204.500 2338 218 207 223 205 213.250 1839 199 193 208 195 198.750 1540 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

180185190195

200205210215

31 32 33 34 35 36 37 38 39 40

Sample

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n UCL

X-bar-bar

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Sample Mean

Range Control Chart

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Sample X-bar Range31 190 199 198 199 196.500 932 224 207 195 192 204.500 3233 186 199 199 209 198.250 2334 211 204 194 202 202.750 1735 217 200 188 200 201.250 2936 204 202 184 195 196.250 2037 193 200 201 205 199.750 1238 211 208 212 173 201.000 3939 205 205 202 211 205.750 940 188 198 178 207 192.750 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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Case #2

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Case #3

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Case #4

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The Process Control “Cycle”Initialization. Take an initial set of N samples with n observations, and use these to compute the initial lower and upper control limits.Step 1. Continue with periodic samples until the process goes out-of-control. Look for an assignable cause.

Step 3. After a process improvement, recalibrate the lower and upper control limits by taking another set of N samples with n observations. Return to Step 1.

Step 2. If possible, improve the process in a manner that decreases the chance that the same assignable cause will reoccur.

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Another Type of Control ChartWe have discussed control charts in the context of a process whose performance is measured by a continuous variable X.For some processes, performance is measured by an binary attribute – 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, you need to use another type of control chart known as a p-chart.

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Control Chart (Handout)