Moving Range (ma + range)
- Last UpdatedMar 19, 2016
- 2 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 the CL, LCL, and UCL for a chart point.
The examples given below illustrate the control limits calculated for chart point 0.0375.
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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 * d2 [Moving Average Span] LCL = CL – (3 * (Estimated Standard Deviation * d3 [Moving Average Span])) UCL = CL + (3 * (Estimated Standard Deviation * d3 [Moving Average Span])) if LCL < 0 then 0; otherwise LCL |
CL = 0.02216 * 1.69257 = 0.03751 The estimated standard deviation calculated from the data is 0.02216 and the d2 factor value for a sample size of 3 is 1.69257. LCL = 0.03751 – (3 * (0.02216 * 0.88837)) = – 0.02155 Since LCL is less than 0, LCL = 0 UCL = 0.03751 + (3 * (0.02216 * 0.88837)) = 0.09655 The d3 factor value for a sample size of 3 is 0.88837. |
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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 = Given Standard Deviation * d2 [Moving Average Span] LCL = CL – (3 * (Standard Deviation * d3 [Moving Average Span])) UCL = CL + (3 * (Standard Deviation * d3 [Moving Average Span])) if LCL < 0 then 0; otherwise LCL |
CL = 0.02025 * 1.69257 = 0.03428 The standard deviation calculated from the data is 0.020254 and the d2 factor value for a sample size of 3 is 1.69257. LCL = 0.03428 – (3 * (0.02025 * 0.88837)) = – 0.01970 Since LCL is less than 0, LCL = 0 UCL = 0.03428 + (3 * (0.02025 * 0.88837)) = 0.08826 The d3 factor value for a sample size of 3 is 0.88837. |
The following tables show examples of control limits and sigma limits for the first 3 chart points and the last chart point using all the data.
|
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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|
1 |
0.07 |
0 |
0.037500 |
0.096547 |
0.0125 |
0.019682 |
|
2 |
0.04 |
0 |
0.037500 |
0.096547 |
0.0125 |
0.019682 |
|
3 |
0.04 |
0 |
0.037500 |
0.096547 |
0.0125 |
0.019682 |
|
... |
||||||
|
13 |
0.0375 |
0 |
0.037500 |
0.096547 |
0.0125 |
0.019682 |
|
Label |
Chart Point |
Use Std. Dev. (sigma est = 1) |
||||
|---|---|---|---|---|---|---|
|
LCL |
CL |
UCL |
Lower σ |
Upper σ |
||
|
1 |
0.07 |
0 |
0.034282 |
0.088262 |
0.011427 |
0.017993 |
|
2 |
0.04 |
0 |
0.034282 |
0.088262 |
0.011427 |
0.017993 |
|
3 |
0.04 |
0 |
0.034282 |
0.088262 |
0.011427 |
0.017993 |
|
... |
||||||
|
13 |
0.0375 |
0 |
0.034282 |
0.088262 |
0.011427 |
0.017993 |