Setting Up and Using a Control Chart Highlights The main reason for analyzing control charts is to determine whether a process is stable or not. •
Control limits must first be calculated from the data collected.
•
Control limits are drawn on the chart and then the data points are plotted.
•
Control chart rules are applied to determine if special causes are making an impact on the process.
In constructing variables control charts, follow this rule: • First make sure the dispersion on the R chart is stable. • If it is, go on to complete the x chart. In constructing attribute control charts, there’s a difference: • Since average and spread are closely related, only one chart is needed.
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Terms Defined in the Glossary • Constant • Square Root • X • X • R • C • U • Over-adjustment • Spike • Cycle • Mixture • Patterns in control charts
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Using a Control Chart to Correct Special Causes of Variation The second part of the SPC Implementation Process is control.
In this course, we will show you the steps to set up an attribute and a variables control chart. If you choose to complete the sample control charts contained in this guide you will need to use a calculator. The calculations are not complicated.
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Calculator Review To brush up on your calculator skills, here are the ways you calculate sums, ranges, average, and square roots. Not all calculators work the same, so check your calculator’s manual if your answers are different. Sum
Range
To add 5 and 3 and 8, do this on your calculator: 1.
Press “5”
2.
Press “+”
3.
Press “3”
4.
Press “+”
5.
Press “8”
6.
Press “=” which gives you “16”
Subtraction is used in figuring range. To figure out the range for the numbers 15, 12, 13, 9, and 6, simply take the highest number of the group (15) and subtract the lowest number (6) of the group. Do this on a calculator: 1. Press “15” (the highest number of the group) 2. Press “-” 3. Press “6” (the lowest number of the group) 4. Press “=” which gives you the range: “9.”
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Average
To figure out the average for this same set of numbers (15, 12, 13, 9 and 6), add up all the numbers, and divide by how many numbers there are (5). Do this on a calculator: 1. Press “15” 2. Press “+” 3. Press “12” 4. Press “+” 5. Press “13” 6. Press “+” 7. Press “9” 8. Press “+” 9. Press “6” 10. Press “=” which gives you “55” 11. Press “ ÷ ” 12. Press “5” 13. Press “=” which gives you the average: “11”
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Square root
The square of a number is the result of multiplying a number times itself. For example, 5 times 5 is 25, 6 times 6 is 36. 25 and 36 are the squares. The square root is the number that is multiplied by itself. The square root of 36 is 6. To figure out the square root for a number, simply push the number, and then push the square root sign “ √ ”. For example, if you want the square root for 16, do this on your calculator: 1. Press “16” 2. Press “ √ ” which gives you the square root: “4” Here’s another example, which will give you an answer with a decimal. If you want to find the square root of 32, do this on your calculator: 1. Press “32” 2. Press “ √ ” which gives you the square root: “5.6568542”
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Calculations on the C Chart
When you first look at a C chart (control chart for attribute data), you may think that it is complex and difficult. But, once the steps are broken out and followed one at a time, the task of completing it is not as hard as it seems. On the next page, you will find a partially filled in C chart that you should remove from this book. You will be asked to fill it in as you progress through the steps required to calculate control limits for a C chart. Again, you may want to write in pencil in case you want to erase and redo your answers. How this calculation process will work
The e-learning course "Setting Up and Using a Control Chart" has a listing of the steps required to complete a variables control chart. As you progress through the steps outlined in the course, complete the chart in this guide. You'll have a partially completed C chart. Columns 1-12 will be filled with data. The training will show you how the different steps are done. At the end of each step, where appropriate, you should complete the final ten columns on your own (columns 16-25). This will give you practice doing each step, helping to make sure you understand it. If you get confused, you will have a chance to review the video segment, study the step in the Student Guide, and check your answers on the partially completed C chart at the end of this step.
So, to begin, remove the C chart worksheet that follows, and begin with Step 1 on the page after that.
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Step 1
Collect Data Write the data onto your C chart. The first 12 columns of your C chart have been filled in. Complete columns 13-25 by copying the data below onto you C chart: Data
Column # 13 14 15 16 17 18 19 20 21 22 22 24 25
68 59 69 65 57 62 73 70 86 60 52 75 57
When you are finished, go to Step 2 in the e-learning course. Step 2
Calculate C To find C , add up all of the numbers in the “Number” row, and divide by how many numbers there are (25). The formula would look like this: Sum of all C Number of C
=
C
Now, calculate C for all 25 columns on your chart.
When you are finished, go to Step 3 in the e-learning course.
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Step 3
Plot C
Notice we have scaled the C chart with the appropriate values. Draw a straight line at 66.6 on your C chart. Label it C .
When you are finished, go to Step 4 in the e-learning course.
Step 4
Calculate the Upper Control Limit (UCL)
C
+3
C
= UCL
The upper control limit for a C chart is determined by adding C to 3 times the square root of C . Now let’s calculate the upper control limit for your C chart. First, take the square root of C (66.6). Then, multiply that number 8.1608823 by 3, and the result is 24.482646. The equation looks like this: 66.6 + 3 (8.1608823) = UCL 66.6 + 24.482646 = 91.1 (rounded off)
When you are finished, go to Step 5 in the e-learning course.
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Step 5
Plot the UCL Draw a dotted line at 91.1 on your C chart. Label it UCL.
When you are finished, go to Step 6 in the e-learning course.
Step 6
Calculate the Lower Control Limit (LCL)
C
-3
C
= UCL
The lower control limit for a C chart is determined by subtracting 3 times the square root of C from C. Now let’s calculate the lower control limit for your C chart. First, take the square root of C (66.6). Then, multiply that number 8.1608823 by 3, and the result is 24.482646. The equation looks like this: 66.6 - 3 (8.1608823) = LCL 66.6 - 24.482646 = 42.1 (rounded off)
When you are finished, go to Step 7 in the e-learning course.
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Step 7
Plot the LCL Draw a dotted line at 42.1 on your C chart. Label it LCL.
When you are finished, go to Step 8 in the e-learning course.
Step 8
Plot the C values Plot all 25 C values on the C chart with dots. Connect the dots with lines. When you are through, check your answer on the next page.
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When you are finished, go to Step 9 in the e-learning course.
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Step 9
Analyze the C chart
You can check for special causes by looking to see whether: • Any point goes outside of the control limits. • There is a run of eight consecutive points either all above or all below C. Is the process in control? As you can tell from analyzing your C chart, there are no special causes operating in the process. So, the process is in control.
Congratulations! Well done. You have successfully completed the C chart.
Return to the e-learning course and continue.
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Calculation on the x and R Chart
When you first look at an x and R chart, you may think it is very complex and difficult. Once the steps are broken out and followed one at a time, the task of completing a chart is not as hard as it seems. On the next page you will find a partially filled in x and R chart, which you should remove from this book. You can fill it in as you progress through the steps required to calculate ranges, control limits, and averages. You might want to write in pencil in case you have to erase and redo your answers. How this calculation process will work
The e-learning course "Setting Up and Using a Control Chart" has a listing of the steps required to complete a variables control chart. As you progress through the steps outlined in the course, complete the chart in this guide. You'll have a partially completed x and R chart. Columns 1-12 will be filled in with data. The training will show you how the different steps are done. At the end of each step, where appropriate, you should complete the final ten columns on your own (columns 16-25).
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This will give you practice doing each step, helping to make sure you understand it. If you get confused, you will have a chance to review the video segment, study the step in this Student Guide, and check your answers on the completed x and R chart included in this guide.
So, to begin, remove the X and R chart worksheet on the following page, and begin with Step 1 on the page after that.
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Collect Data. Write the data onto your x and R chart.
Step 1
Here are the measurements taken from 10/23 to 10/26:
10/23 10/23 10/23 10/23 10/24 10/24 10/24 10/24 10/25 10/25 10/25 10/25 10/26 8:00 10:00 12:00
2:00
8:00 10:00 12:00
2:00
8:00 10:00 12:00
2:00
8:00
SK
SK
SK
SK
SK
SK
SK
SK
SK
SK
SK
SK
SK
.70
.65
.85
.75
.75
.75
.65
.60
.50
.65
.85
.65
.65
.70
.70
.75
.80
.70
.70
.65
.60
.55
.85
.70
.60
.70
.75
.85
.80
.75
.90
.60
.85
.65
.65
.70
.80
.65
.70
.75
.75
.70
.80
.70
.70
.65
.60
.80
.70
.70
.60
.60
.70
.60
.85
.65
.75
.60
.70
.65
.80
.80
.70
.70
.65
Enter this data on columns 13-25 of the blank chart you have removed from this book.
When you are finished, go to Step 2 in the e-learning course.
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Step 2
Calculate the Range (R) of each sample.
The last row of the columns is labeled “Range R.” You have seen in your calculator review and in the interactive training how to calculate the range. (Simply subtract the lowest number in the sample from the highest number). Example
Here is a picture and the calculation for the first column:
Date Time Operator Sample Measurements
10/20
8:00
1. 2. 3. 4. 5.
Sum Average X Range R
SK .65 .70 .65 .65 .85
.20
Highest minus lowest equals range. .85
-
.65
=
.20
(The highest Number)(minus)(The Lowest Number) (Range)
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The range for the first column is .20. Now, calculate the ranges for columns 13-25.
Check your answers against the numbers in the right-hand column:
Column # 13 14 15 16 17 18 19 20 21 22 23 24 25
High 0.75 0.85 0.85 0.80 0.90 0.75 0.85 0.65 0.80 0.85 0.85 0.70 0.70
-
Low 0.70 0.60 0.70 0.65 0.70 0.60 0.65 0.60 0.50 0.65 0.70 0.60 0.60
= = = = = = = = = = = = = =
Range 0.05 0.25 0.15 0.15 0.20 0.15 0.20 0.05 0.30 0.20 0.15 0.10 0.10
When you are finished, go to Step 3 in the e-learning course.
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Step 3
Calculate R . You have seen that the last row of the columns is labeled “Range R.” To find the average of all the range values (or, “R”), simply add up all of the ranges and divide by how many ranges there are (25). The formula would look like this:
Sum of all R Number of R
=
R
Now, calculate R for all 25 columns on your chart.
When you are finished, go to Step 4 in the e-learning course.
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Step 4
Plot R on the range chart.
Notice that we have scaled the R chart with appropriate values. Draw a straight line at .178 on your R chart. Label it R .
Ranges .40 .30 .20 .10 0
When you are finished, go to Step 5 in the e-learning course.
Step 5
Calculate the Upper Control Limit for range:
R x D4 = UCL Reproduced here is the “Table of Constants for xr and R Charts”* from a standard reference book on SPC. The important thing for you to know is that this table helps you calculate the upper and lower control limits for your chart. Since the size of our sample is five (one sample includes five measurements), we will be looking at the row under D4 with “5” in the sample column. We have boxed in the correct row for you.
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Table of Constants for X and R Charts Divisors for Estimate of Sample Standard Factors for Control Limits Deviation Size D3 D4 d2 n A2 2 1.880 0 3.267 1.128 3 1.023 0 2.574 1.693 4 0.729 0 2.282 2.059 5 0.577 0 2.114 2.326 6 0.483 0 2.004 2.534 7 0.419 0.076 1.924 2.704 8 0.373 0.136 1.864 2.847 9 0.337 0.184 1.816 2.970 10 0.308 0.223 1.777 3.078 * Constants explained: Each of the calculations for R and x control limits uses a formula that incorporates constants, labeled A2, D3, or D4. These are values already determined from a standard table of quality control statistics. They change according to the sample size used. When limits are calculated in this way, the averages and ranges of the next samples will fall within these limits if the variation is due to common cause (natural fluctuation) alone.
Here is the formula for calculating the upper control limit (UCL):
R x D4 = UCL Now let’s calculate the upper control limit for your R chart: .178 (R)
x 2.114 (Times) (D4 from Table)
=
? (UCL)
You may check your answer by referring to Step 5 in the elearning course.
When you are finished, go to Step 6 in the e-learning course. Applying SPC – Setting Up and Using a Control Chart
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Step 6
Draw and label the upper control limit on the range chart.
Draw a dotted line at .376 on your R chart. Label it UCL.
When you are finished, go to Step 7 in the e-learning course. Step 7
Calculate the Lower Control Limit (LCL):
R x D3 Reproduced again below is the “Table of Constants for x and R charts,” with the correct row boxed. In calculating lower control limits for range, use constant D3:
Table of Constants for X and R Charts Divisors for Estimate of Sample Standard Size Factors for Control Limits Deviation D3 D4 d2 n A2 2 1.880 0 3.267 1.128 3 1.023 0 2.574 1.693 4 0.729 0 2.282 2.059 5 0.577 0 2.114 2.326 6 0.483 0 2.004 2.534 7 0.419 0.076 1.924 2.704 8 0.373 0.136 1.864 2.847 9 0.337 0.184 1.816 2.970 10 0.308 0.223 1.777 3.078
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Now let’s calculate the lower control limit:
R
0.178 (R)
x
D3
=
LCL
x 0 (Times) (D3 from Table)
=
? (LCL)
When you are finished, go to Step 8 in the e-learning course. Step 8
Draw and label the lower control limit on the range chart. Draw a dotted line at 0 on your R chart. Label it LCL.
When you are finished, go to Step 9 in the e-learning course. Step 9
Plot the R values. Plot all 25 R values on the R chart using dots. Connect the dots with lines. Your chart should look like the chart on the next page.
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When you are finished, go to Step 10 in the e-learning course
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Step 10
Analyze the R chart. You can check for special causes by looking to see whether: •
Any point goes outside of the control limits.
•
There is a run of eight consecutive points either all above or all below R .
Are any special causes affecting the process? As you can tell from analyzing your R chart, there are no special causes operating in the range chart. The R chart is in control.
Congratulations! You’ve successfully completed the R chart! When you are finished, go to Step 3 in the e-learning course. Step 11
Calculate x values (averages) on the x and R chart. You have seen in your calculator review and in the interactive training course how to calculate the average. (Simply add the five sample measurements together and divide by five).
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Here is a picture and the calculation for the first column: Date Time Operator Sample Measurements
10/20
8:00
1. 2. 3. 4. 5.
Sum Average X Range R
SK .65 .70 .65 .65 .85 3.50 .70 .20
.65 + .70 + .65 + .65 + .85 = 3.50 3.5 ÷ 5 = .70 The x (average) for the first column is .70. Now, calculate the averages for the remaining 13 columns (13-25) directly on your chart. First add all the sample measurements together and write the total in the row marked “Sum.” Then divide that number in each column by five and write the result in the row marked “Average x .” When you are through, check your answers by referring to the e-learning course.
When you are finished, go to Step 12 in the e-learning
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Step 12
Calculate X . To find the average of the averages (or, X ), simply add up all of the averages and divide by how many averages there are (25). The formula would look like this:
Sum of all x Number of x
=
X
Now, calculate X for all 25 columns on your chart.
When you are finished, go to Step 13 in the e-learning
Step 13
Draw and label X on the x chart. Notice we have scaled the x chart with appropriate values. Draw a straight line at .716 on your x chart. Label it X .
When you are finished, go to Step 14 in the e-learning
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Step 14
Calculate the Upper Control Limit:
X + (A2 x R ) = UCL Reproduced again is the "Table of Constants for x and R Charts." As you saw with the ranges, this table helps you calculate the upper and lower control limits for your chart. Because the size of our sample is five, we will be looking at the row with "5" in the column under A2. The correct row is boxed for you.
Table of Constants for X and R Charts Divisors for Estimate of Sample Standard Factors for Control Limits Deviation Size D3 D4 d2 n A2 2 1.880 0 3.267 1.128 3 1.023 0 2.574 1.693 4 0.729 0 2.282 2.059 5 0.577 0 2.114 2.326 6 0.483 0 2.004 2.534 7 0.419 0.076 1.924 2.704 8 0.373 0.136 1.864 2.847 9 0.337 0.184 1.816 2.970 10 0.308 0.223 1.777 3.078
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Now let's calculate the upper control limit. Remember, the formula is as follows:
X
+
(A2 x
R)
=
UCL
X is 0.716 0.577 (A2 from Table)
x (Times)
0.178 (R)
= 0.102706
So, 0.716 (X)
+
0.102706
(Plus) (From Previous Equation)
=
? UCL
When you are through, check your answer by referring to the e-learning course.
When you are finished, go to Step 15 in the e-learning Step 15
Draw and label the Upper Control Limit on the x chart. Draw a dotted line at .819 on your x chart. Label it UCL.
When you are finished, go to Step 16 in the e-learning
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Step 16
Calculate the lower control limit (LCL):
X
−
(A2 x
R)
=
LCL
Reproduced again is the "Table of Constants for x and R Charts." With a box around the row for our sample size. Use A2 for this calculation.
Table of Constants for X and R Charts Divisors for Estimate of Sample Standard Size Factors for Control Limits Deviation D3 D4 d2 n A2 2 1.880 0 3.267 1.128 3 1.023 0 2.574 1.693 4 0.729 0 2.282 2.059 5 0.577 0 2.114 2.326 6 0.483 0 2.004 2.534 7 0.419 0.076 1.924 2.704 8 0.373 0.136 1.864 2.847 9 0.337 0.184 1.816 2.970 10 0.308 0.223 1.777 3.078
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Now let’s calculate the Lower Control Limit:
X
is 0.716 0.577
x
0.178
(A2 from Table)
(Times)
(R)
=
?
So, 0.716
-
0.102706
=
( X ) (Minus) (From Previous Equation)
? LCL
When you are through, check your answer by referring to the e-learning course.
When you are finished, go to Step 17 in the e-learning
Step 17
Draw and label the lower control limit on the x chart. Draw a dotted line at 0.613 on your x chart. Label it LCL.
When you are finished, go to Step 18 in the e-learning
Step 18
Plot the x values. Plot all 25 x values on the x chart with dots. Connect the dots with lines. Check your answers on the following page.
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When you are finished, go to Step 19 in the e-learning course.
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Step 19
Analyze the x chart for special causes.
As you did with the R chart, you can check for special causes by looking to see whether; • Any point goes outside of the control limits. • There is a run of eight consecutive points either all above or all below X . Is the x chart in control? Is the process in control? As you can tell from analyzing your x and R chart, there are no special causes operating in the averages chart. So, since the R chart is also in control, the process is in control.
Congratulations! Well done. You have successfully completed the X and R chart.
Go back to the e-learning course and continue.
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Using a Control Chart: Interpretation and Action
Operators can take certain actions to begin solving problems and reducing variation in the process. • There are certain tools and techniques operators can use to help identify problems and begin to identify causes of variation. • There are also a number of ways to take an action if the problem and cause of variation are known.
Control charts are valuable tools because they can tell us whether variation is due to common or special causes. • Data points can form patterns that you will be able to recognize the longer you work with control charts. • Some patterns are natural and are not cause for concern. Other patterns, however, should alert you to the possibility that special causes are at work.
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Once you have uncovered a problem, Pareto charts and fishbone diagrams can be used to find the causes of the variation. • Pareto charts show you how often defects occur, and put them in order of importance. • Fishbone diagrams help you categorize, graphically, the variables in the process. This will in turn help you focus your attention on potential causes of variation.
There are things you should and should not do as an operator once you have found the causes of variation. • Action, whether it is taken by you or the team needs to be taken to correct the shift in the process. • Action taken without knowing the source of the special cause may lead to over-adjustment.
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Identifying Problems and Causes: Control Chart Patterns Control charts are a powerful indicator of process problems coming from special causes. Some control chart patterns suggest there are special causes at work. Note that the problems due to special causes tell us there is a problem of immediate concern. If a process has shifted, you'll see evidence of this on a control chart. Different control chart patterns tell different stories. When there is evidence of a process shift, the cause must be investigated immediately. Some of the patterns you may see are shown below. Natural patterns
A natural pattern is one that gives no evidence of unnaturalness over a long series of plotted points. Natural patterns are stable and reflect no trends or shifts. There are no special causes disturbing the process.
UCL
Process Average
LCL
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Points outside the control limit
Points outside the control limits indicate a special cause. Immediate investigation is called for to correct the condition.
Runs of eight
Eight points in a row either all above or all below the process average is evidence of a special cause. These runs should be investigated.
UCL
Process Average
LCL
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Additional patterns
There are additional patterns that can be interpreted as indicators of process problems.
Cycles
Description: Cycles are short patterns in the data that occur over and over. Since this pattern is not random, some special cause may be affecting the process.
UCL
Process Average
LCL
Possible causes: The causes of cycles can be variables that come and go on a regular basis. For example, movements and changes of position, variations in shift, or time of day may cause cycles.
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Mixtures
Description: A mixture pattern shows data points falling at the high and low control limits, but without normal fluctuations near the center. Mixtures have unnaturally long lines joining points.
UCL
Process Average
LCL
Possible causes: Mixtures could be caused by a combination of two different patterns on the same chart -one at a high level and one at a low level; for example, two different measuring tools, two separate lots of raw material, or two different operators taking turns.
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Spikes
Description: From time to time you may find that a data point falls outside of a control limit. In the "real world" of manufacturing, this happens occasionally. One data point outside a control limit should tell you that something could be wrong, not that something is wrong.
UCL
Process Average
LCL
Possible causes: There may not be an assignable cause. Spikes do not always mean that the process is out of control. Nor are they always the result of special causes. In fact, the chances are about 3 in 1,000 that you will get a spike in a process that is in control. They should alert you to keep a close watch on the process, but do not always mean you need to adjust the process at this point.
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Identifying Problems and Causes: Pareto Charts and Fishbone Diagrams Pinpointing causes
Control charts are a useful tool in helping determine if a problem exists and, sometimes, in finding the cause. A way to pinpoint causes once a problem has been uncovered is to use Pareto charts and fishbone diagrams. These tools are also useful in helping determine where variation may be coming from.
Pareto charts
Pareto charts show the frequency of defects, and put them in order of magnitude -- separating the few very important defects from the more numerous, less important ones. This puts things into perspective and focuses your attention on the biggest and most urgent problems. You may recognize the Pareto chart shown below from a previous exercise: 60 50 Number of complaints
40 30 20 10 0 Parking problems
Rude waiters
Cooking problems
Type of customer complaint
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Fishbone diagrams
Fishbone diagrams display cause and effect relationships. Parameters affecting the process are listed in logical categories such as: • Materials • Methods • Manpower • Machines • Measurements • Environment Examining fishbone diagrams can help you understand what might be causing variation in the process.
Manpower
Methods
Materials
Process 1
1st Shift
Raw Material 1
Process 2
Raw Material 2
Machines
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3rd Shift
Quality
Machine 1 Machine 2
2nd Shift
Measurement 1 Measurement 2
Temp Humidity Lightning Storm
Measurements
Environment
Applying SPC – Setting Up and Using a Control Chart
Implementing and Sustaining Action Rationale
When you've been able to identify the special causes of variation, whether by observing them yourself or by analysis and experimentation by the SPC teams, action must be taken to correct the process shift or special cause. If you and your SPC team are able to correct a special cause of variation, you need to make sure that correction works. Again, the control charts will help you see if the process is back on track, and if it isn't, you need to look further into the cause. Any delay may mean unnecessary amounts of scrap are produced, reducing yields and adding to cost. A delay may hide the source of the special cause; the time to investigate special causes is when those causes are active. Action may be taken by the: • Operator • SPC team It's important to realize that the members of the SPC team can sometimes discover problems together, and can do a lot more to improve the process than individuals could do. Let's look at each set of actions separately.
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Taking action 1. Routine operator planning
2. Immediate investigation of special causes
It is important that operators plot their own control charts, under the guidance of the SPC team and the SPC expert. SPC programs tend to be short-lived and ineffective when people not involved with the process take over the job of plotting and maintaining the charts. Allowing operators to plot charts means the charts become a tool for managing the workstation.
As an operator, if you see that the process is changing you should immediately look to see where the problem lies. Make an immediate check of: • The control chart: Has the data been entered correctly? • The process: Is this the only time the special cause occurred? • The product: Is there a specific defect? • The measurement tools: Are they calibrated? Is the control plate or standard being used properly? • The environment: Check the temperature, the dust content of the air, the humidity, the lighting, etc. • The methods used: Has anything changed recently? • The operator: Who is operating the equipment? Is that person trained? Was a procedure left out? If you are able to figure out the cause of your problem and are confident that you can correct it, then do it! Don't forget to make a note of what action you've taken on the control chart, or in a comment field in a computer-based control chart. The information may be helpful at a later date.
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Applying SPC – Setting Up and Using a Control Chart
3. If the cause is unknown
If you don't know the cause, you should immediately: • Notify the SPC driver and / or the lead manager. This information may instigate an immediate meeting of the SPC team or a subset of the SPC team for that shift. • Record the action taken and when it was taken on the control chart. The next shift can then see what was done.
4. If operator can't take corrective action
• If the operator knows the correct action to take but can't take it, the operator will bring the problem to the attention of the SPC driver and / or the SPC team -whatever is appropriate to the situation. • If the correct action is not known, the SPC driver and / or the SPC team must determine what it should be with the assistance of the SPC expert, engineers, or managers.
5. If the SPC team can't identify action to take
If the correct action is still not known, the SPC team may seek special help in conducting a statistically designed experiment to uncover complex cases. Such a statistically designed experiment, developed with the help of SPC experts, will help pinpoint the source of trouble. Also make sure that: • You keep a record of causes and actions taken. What is discovered on one chart about causes is often useful in other situations.
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The next step: reducing common causes
Process capability-- a future SPC challenge
Once special causes have been controlled, it is possible to determine process capability and eventually reduce common causes of variation. As we mentioned earlier, improving process capability that results in narrower control limits means reexamining how machines are used, what measuring or counting techniques are employed, what steps the operator uses, and the like. This takes time and generally means redesigning the process. Nevertheless, the ultimate goal of SPC is constant improvement of the process. Your SPC team, after eliminating special causes may feel it appropriate to address common causes -- to improve the process to narrow the control limits and reduce the fluctuation in the system. You'll probably work with your SPC Expert and several others at the site to make it happen. Even if your team decides not to address common causes, eliminating special causes of variation is a significant accomplishment. If you get this far, you can be proud of your team for winning the fight over variation!
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Applying SPC – Setting Up and Using a Control Chart
Activity 1
Purpose
The purpose of this activity is to give you practice identifying and comparing various patterns that you may see in your control charts. You will also practice other lessons from this training.
Instructions
In the space provided, answer the following questions, thinking back on the lessons you learned in this training. Check your answers with those that follow.
The point
The point of this activity is to reinforce your understanding of how control charts can be interpreted. 1.Pareto charts and fishbone diagrams are techniques that can help you identify the causes of variation in your process. (circle one)
True
False
2.What do we call a pattern of data points that gives us no evidence that there is anything unusual going on in the process? (circle one)
Natural pattern False calls Run Cycle
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3.What do we call a short pattern of data points that occurs over and over? (circle one) Mixture Cycle Run 4.Which of the two techniques would you use to separate the few, very important defects from the more numerous, less important ones? (circle one)
Pareto chart
Fishbone diagram
5.If you have been able to identify the causes of variation (either by yourself or with the SPC team), you should under no circumstances take any action to correct the process shift or special causes. (circle one)
True
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False
Applying SPC – Setting Up and Using a Control Chart
Answers to Activity 1
1.Pareto charts and fishbone diagrams are techniques that can help you identify the causes of variation in your process. (circle one) True
False
2.What do we call a pattern of data points that gives us no evidence that there is anything unusual going on in the process? (circle one) Natural Pattern False calls Run Cycle
3.What do we call a short pattern of data points that occurs over and over? (circle one)
Mixture Cycle Run 4.Which of the two techniques would you use to separate the few, very important defects from the more numerous, less important ones? (circle one) Pareto Chart
Fishbone diagram
5.If you have been able to identify the causes of variation (either by yourself or with the SPC team), you should under no circumstances take any action to correct the process shift or special causes. (circle one)
True
Applying SPC – Setting Up and Using a Control Chart
False
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Statistical Process Control Applying SPC Glossary
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Applying SPC -- Glossary
Glossary Attribute data Data that can be counted, or recorded simply as yes/no, pass/fail, or go/no-go. Attribute data is often gathered as the number of defects, defects per unit, percentage defective, or number defective.
Average The sum of a group of numbers divided by how many numbers there are. The symbol used for the average is a bar ( ) placed over the letter, as in X bar or x .
Board pinning The operation that manufactures a board with soldered pins, which are used in computers. Electronic card assemblies are connected to the pinned board.
C The process average line on a C chart. (Spoken as C bar.)
C chart An attribute control chart on which the number of defects in a sample is plotted. For a C chart, the sample size must always be the same.
Capable/capability The extent to which a stable process is able to meet specification. Central tendency The center or middle of a distribution, often described as an average or mean.
Common cause A natural kind of variation that comes from the normal ups and downs of a process. When analyzing control charts it is seen as data points, all within control limits. (See also Special cause.)
Constant A value that does not change. In this course, you will see constants used in calculating control limits.
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Contamination Dirt particles, or other foreign material that can cause defects in a manufacturing process.
Control chart A graph of a process that has: • Plotted data • A process average line • One or two control limits It is used to help determine whether a process is stable as well as to aid in maintaining control.
Control limit A line (or lines) on a control chart used to tell if a process is stable or shifting. A point beyond a control limit shows that special causes are probably affecting the process. Control limits are calculated from data collected from the process and are not to be confused with engineering specifications.
Cycle A pattern in a control chart that keeps repeating. Cycles show a short-term effect happening over and over again.
Data A number or piece of information from a process. SPC data in this course can be attribute or variables data.
Defective unit A product or unit that fails to meet the product specifications.
Detection method A method of quality control in which products are checked for meeting specs after they are made. The defective items are then rejected. If the defect rate gets too high, the process is adjusted. In this method, parameters that help make the product are not monitored. This is an old-style method of quality control that tries to find a bad product after it has been made. (See Prevention method.) Page 114
Applying SPC – Glossary
Dispersion The amount of spread in a distribution. Dispersion can be narrow and tightly clustered around the center. Or it can be wide, going out far on each side from the center.
Distribution A way of describing the variation in a process, or the pattern in a group of data. This distribution pattern can be described in terms of its: • Location • Spread • Shape Location is usually described by the central tendency (mean or average, or median). Spread is usually described by the standard deviation or the range. Shape involves things such as the number of peaks.
Experiment In order to be done correctly, an experiment should be statistically designed. Different process parameters are varied from high to low values. The effect on quality is then studied using powerful statistical methods. When done right, the experiment can show how to make a process the best it can be.
Fishbone diagram A cause and effect diagram that shows the different process parameters in a sensible way. Histogram A type of graph showing data values on one axis and frequency on the other. When plotted, the data forms a shape with a central tendency and a certain amount of dispersion.
In spec Meets spec limits.
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Location Where the central tendency of the data is; often described by the average.
Mean Average; often used as the label for the process average line on a control chart.
Mixture Pattern on a control chart with too many points near the control limits; not very many points fall close to the mean.
Nonconforming units Units that do not conform to a spec limit; sometimes called defective units. Not capable The spread of a process that is too wide when compared to the spec limits.
NP chart An attribute chart on which the number of defective is plotted.
Out of spec Defective; nonconforming; does not meet spec limits.
Over-adjustment An over-adjustment happens when a change is made to a process that shifts it out of control in the direction of the change. Usually, the adjustment made either was too large, or was not really needed in the first place.
P chart An attribute control chart on which percentages are plotted. Usually seen as percentage defective charts.
Parameter A process element that is measured or counted. For example, in a photo mask process, line width is one parameter, and concentration of an acid solution may be another. Other parameters might be the number of bent pins, the humidity in a clean room, etc.
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Applying SPC – Glossary
Pareto chart A simple tool for problem-solving that ranks problems from those that happen most often to those that happen least often.
Patterns (in control charts) The advantage of control charts is that they show data points in relation to control limits over a period of time. These data points form a pattern that can help you tell how a process is doing. For example, control chart patterns will show if a process is stable or shifting. Photo mask house A manufacturing line that produces glass photo masks, which are used in the production of semiconductor computer chips.
Prevention method A method of quality control that means using SPC to monitor and control many process parameters that go into making a product. This is an efficient method of quality control that controls the process itself, in contrast to the old detection method.
Process A system of elements that work together to produce something.
Process average The overall average of a set of values: the centerline on a control chart.
Process spread How far data points go out on each side from the middle of a process.
R The process average line on the R chart. (Spoken as R bar.)
Range The highest value minus the lowest value in a sample. It is a way to describe spread, or dispersion. Applying SPC – Glossary
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Run A consecutive number of points all above or all below the process average. It can be evidence that special causes of variation are at work if the run is eight or greater.
Sample A small group of data taken at about the same time. In this course, it means the same as subgroup.
Shape What a distribution looks like.
SPC driver A production employee who has extra responsibility for SPC in the manufacturing line.
SPC expert An individual who has a lot of statistical knowledge. Calculates control limits for the manufacturing line, serves as SPC tutor for this course.
SPC Implementation Process The series of activities including self-study learning and implementation meetings with SPC team members. Involves choosing parameters to control, collecting data, calculating control limits, and perhaps even improving process capability. Special cause A type of variation that is shown by a point beyond the control limits or a run of eight points within the control limits. It means something special has happened to the process to make it shift or change.
Spec/specification The engineering requirement for judging if a part is good or bad. Specifications and spec limits should never be confused with control limits.
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Applying SPC – Glossary
Spike A single point beyond a control limit when the process has not really shifted. In the real world, this happens occasionally. It is telling you that something could be wrong with the process, not that the process is definitely wrong.
Spread How far out from the middle the data points go on each side in a distribution.
Square root A number that, when multiplied by itself, gives the required number. For example, 3 is the square root of 9. The square root of 25 is 5.
Stability A process is stable, or in control, when no special causes of variation are found on the control chart. (See also Statistical control.)
Standard deviation A way to describe the spread of a process. Statistical control When all special causes of variation are gone and only common causes are left.
Statistically designed experiment An experiment that involves changing process or tool settings in a systematic fashion. Math and statistical methods are used in the design and analysis phases so that the best combination of settings can be found. Statistical Process Control (SPC) Using control charts to help keep a process stable and improve its capability. It eliminates special cause variation by finding the root cause of the problem. U The process average line on a U chart. (Spoken as U bar.)
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U chart An attribute control chart on which defects per group or unit are plotted.
Variables data Data obtained from measurements. Examples include the diameter of a bearing in millimeters, the weight of a door in kilograms, or the length of a line in microns.
Variation The difference between individual values in a process.
X Symbol for average or mean. (Spoken as X bar.) It is a data value plotted on an x chart.
X The average of the averages of a number of samples. (Spoken as X double-bar.) It is the process average line on an x chart.
X and MR chart A variables control chart having two separate charts. One is for individual measurements and the other is for the moving range.
X and R chart A popular variables control chart having two separate charts. One is for plotting averages and the other is for ranges.
X and S chart A variables control chart having two separate charts. One is for averages and the other is for standard deviations.
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Applying SPC – Glossary
