Moving Average (ma + sigma)
- Last UpdatedMay 16, 2023
- 3 minute read
The LCL and UCL are calculated based on the sigma setting for a characteristic. The tables below contain the formulas used to calculate CL, LCL, and UCL for a chart point.
The example given below illustrates the control limits calculated for the chart point 0.9525.
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Use Tables (sigma est = 0) |
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|---|---|
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Formula |
Example |
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CL = LCL = CL – (3 * ASTD) UCL = CL + (3 * ASTD) The adjusted standard deviation from the estimated standard deviation is ASTD. |
The estimated standard deviation calculated from the data is 0.02162 and the moving average span configured for a characteristic is 3. CL = 0.95577, where 0.95577 is the moving average bar calculated from the data. LCL = 0.95577 – (3 * 0.01248) = 0.91833 UCL = 0.95577 + (3 * 0.01248) = 0.993212 |
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Use Std. Dev. (sigma est = 1) |
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|---|---|
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Formula |
Example |
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CL = Mean LCL = CL – (3 * ASTD) UCL = CL + (3 * ASTD) The adjusted standard deviation from the calculated standard deviation is ASTD. |
The standard deviation calculated from the data is 0.02025 and the moving average span configured for a characteristic is 3. CL = 0.95267 LCL = 0.95267 – (3 * 0.01169) = 0.91759 UCL = 0.95267 + (3 * 0.01169) = 0.98775 |
The following tables show examples of control limits and sigma limits for the first three chart points and the last chart point using all the data.
|
Label |
Chart Point |
Use Tables (sigma est = 0) |
||||
|---|---|---|---|---|---|---|
|
LCL |
CL |
UCL |
Lower σ |
Upper σ |
||
|
1 |
0.948333 |
0.918326 |
0.955769 |
0.993211 |
0.012481 |
0.012481 |
|
2 |
0.958333 |
0.918326 |
0.955769 |
0.993211 |
0.012481 |
0.012481 |
|
3 |
0.96 |
0.918326 |
0.955769 |
0.993211 |
0.012481 |
0.012481 |
|
... |
||||||
|
13 |
0.9525 |
0.918326 |
0.955769 |
0.993211 |
0.012481 |
0.012481 |
|
Label |
Chart Point |
Use Std. Dev. (sigma est = 1) |
||||
|---|---|---|---|---|---|---|
|
LCL |
CL |
UCL |
Lower σ |
Upper σ |
||
|
1 |
0.948333 |
0.917585 |
0.952667 |
0.987748 |
0.011694 |
0.011694 |
|
2 |
0.958333 |
0.917585 |
0.952667 |
0.987748 |
0.011694 |
0.011694 |
|
3 |
0.96 |
0.917585 |
0.952667 |
0.987748 |
0.011694 |
0.011694 |
|
... |
||||||
|
13 |
0.9525 |
0.917585 |
0.952667 |
0.987748 |
0.011694 |
0.011694 |