Moving Sigma (ma + ms)
- Last UpdatedMay 16, 2023
- 3 minute read
The CL, 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 examples given below illustrate the control limits calculated for the chart point 0.01887.
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Use Tables (sigma est = 0) |
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|---|---|
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Formula |
Example |
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CL = Estimated Standard Deviation * C4 [Moving Average Span] LCL = CL – (3 * Estimated Standard Deviation * UCL = CL + (3 * Estimated Standard Deviation * if LCL < 0 then 0; otherwise LCL |
CL = 0.02162 * 0.88623 = 0.01916 The estimated standard deviation calculated from the data is 0.02162 and the C4 factor value for the moving average span of 3, which is configured for this characteristic is 0.88623. LCL = (0.01916) – 3 * (0.02162 * Since LCL is less than 0, LCL = 0 UCL = (0.01916) + 3 * (0.02162 * |
)
= –0.01089
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Use Std. Dev. (sigma est = 1) |
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|---|---|
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Formula |
Example |
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L = Standard Deviation * [Moving Average Span] LCL = CL – (3 * Standard Deviation * UCL = CL + (3 * Standard Deviation * if LCL < 0 then 0; otherwise LCL |
CL = 0.02025 * 0.88623 = 0.01795 The standard deviation calculated from the data is 0.02025 and the C4 factor value for the moving average span of 3, which is configured for the characteristic is 0.88623. LCL = (0.01795) – 3 * (0.02025 * Since LCL is less than 0, LCL = 0 UCL = (0.01795) + 3 * (0.02025 * |
The following tables show examples of control limits and sigma limits for all the chart points using all the data.
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Label |
Chart Point |
Use Tables (sigma est = 0) |
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|---|---|---|---|---|---|---|
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LCL |
CL |
UCL |
Lower σ |
Upper σ |
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|
13 |
018875 |
0 |
0.019158 |
0.049201 |
0.006386 |
0.010014 |
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Label |
Chart Point |
Use Std. Dev. (sigma est = 1) |
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|---|---|---|---|---|---|---|
|
LCL |
CL |
UCL |
Lower σ |
Upper σ |
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|
13 |
018875 |
0 |
0.017949 |
0.040698 |
0.005983 |
0.009383 |