Moving Range (ix + mr)
- Last UpdatedMar 19, 2016
- 2 minute read
The CL, LCL, and UCL are calculated based on the sigma setting for a characteristic. In a moving range chart, the range is always between 2 measurements, hence the d2 factor is always 2. The tables below contain formulas to calculate the CL, LCL, and UCL for a chart point. A chart point is the absolute difference between an individual reading (measurement data) and the individual reading collected prior to this reading for a characteristic.
The example given below illustrates the control limits calculated for chart point 0.015.
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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[2] LCL = CL – (3 * (Estimated Standard Deviation * d3[2])) UCL = CL + (3 * (Estimated Standard Deviation * d3[2])) if LCL < 0 then 0; otherwise LCL |
CL = 0.02247 * 1.12838 = 0.02535 The estimated standard deviation calculated from the data is 0.02247 and is the d2 factor value for a sample size of 2 is 1.12838. LCL = 0.02538 – (3 * (0.02248 * 0.85250)) = – 0.03212 Since LCL is less than 0, LCL = 0 UCL = 0.02538 + (3 * (0.02247 * 0.85250)) = 0.08283 The d3 factor value for a sample size of 2 is 0.85250. |
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Use Std. Dev. (sigma est = 1) |
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Formula |
Example |
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CL = Standard Deviation * d2[2] LCL = CL – (3 * (Standard Deviation * d3[2])) UCL = CL + (3 * (Standard Deviation * d3[2])) if LCL < 0 then 0; otherwise LCL |
CL = 0.02025 * 1.12838 = 0.02285 The standard deviation calculated from the data is 0.02025 and the d2 factor value for a sample size of 2 is 1.12838. LCL = 0.02285 – (3 * (0.02025 * 0.85250)) = – 0.02895 Since LCL is less than 0, LCL = 0 UCL = 0.02285 + (3 * (0.02025 * 0.85250)) = 0.07466 The d3 factor value for a sample size of 2 is 0.85250. |
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) |
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|---|---|---|---|---|---|---|
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LCL |
CL |
UCL |
Lower σ |
Upper σ |
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|
1 |
- |
- |
- |
- |
- |
- |
|
2 |
0.045 |
0 |
0.025357 |
0.082830 |
0.008452 |
0.019158 |
|
3 |
0.025 |
0 |
0.025357 |
0.082830 |
0.008452 |
0.019158 |
|
... |
||||||
|
15 |
0.015 |
0 |
0.025357 |
0.082830 |
0.008452 |
0.019158 |
|
Label |
Chart Point |
Use Std. Dev. (sigma est = 1) |
||||
|---|---|---|---|---|---|---|
|
LCL |
CL |
UCL |
Lower σ |
Upper σ |
||
|
1 |
- |
- |
- |
- |
- |
- |
|
2 |
0.045 |
0 |
0.022855 |
0.074655 |
0.007618 |
0.017267 |
|
3 |
0.025 |
0 |
0.022855 |
0.074655 |
0.007618 |
0.017267 |
|
... |
||||||
|
15 |
0.015 |
0 |
0.022855 |
0.074655 |
0.007618 |
0.017267 |