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 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 [Sample Size] LCL = CL – (3 * (Estimated Standard Deviation * d3 [Sample Size])) UCL = CL + (3 * (Estimated Standard Deviation * d3 [Sample Size])) if LCL < 0 then 0; otherwise LCL |
CL = 0.02205 * 2.05875 = 0.045391 The estimated standard deviation calculated from the data is 0.02205 and the d2 factor value for a sample size of 4 is 2.05875. LCL = 0.04539 – (3 * 0.02205 * 0.87981)) = – 0.01280 Since LCL is less than 0, LCL = 0 UCL = 0.04539 + (3 * (0.02205 * 0.87981)) = 0.10358 The d3 factor value for a sample size of 4 is 0.87981. |
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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 = Standard Deviation * d2 [Sample Size] LCL = CL – (3 * (Standard Deviation * d3 [Sample Size])) UCL = CL + (3 * (Standard Deviation * d3 [Sample Size])) if LCL < 0 then 0; otherwise LCL |
CL = 0.02025 * 2.05875 = 0.04170 The standard deviation calculated from the data is 0.02025 and the d2 factor value for a sample size of 4 is 2.05875. LCL = 0.04170 – (3 * (0.02025 * 0.87981)) = – 0.01176 Since LCL is less than 0, LCL = 0 UCL = 0.04170 + (3 * (0.02025 * 0.87981)) = 0.09516 The d3 factor value for a sample size of 4 is 0.87981. |
The following tables show examples of control limits and sigma limits for all the chart points 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 |
0.051281 |
0.108434 |
0.017094 |
0.019051 |
|
2 |
0.06 |
0 |
0.037317 |
0.096076 |
0.012439 |
0.019586 |
|
3 |
0.0075 |
0 |
0.037317 |
0.096076 |
0.012439 |
0.019586 |
|
4 |
0.0375 |
0 |
0.045391 |
0.103584 |
0.015130 |
0.016895 |
|
Label |
Chart Point |
Use Std. Dev. (sigma est = 1) |
||||
|---|---|---|---|---|---|---|
|
LCL |
CL |
UCL |
Lower σ |
Upper σ |
||
|
1 |
0.07 |
0 |
0.047110 |
0.099614 |
0.015703 |
0.017501 |
|
2 |
0.06 |
0 |
0.034282 |
0.088262 |
0.011427 |
0.017993 |
|
3 |
0.0075 |
0 |
0.034282 |
0.088262 |
0.011427 |
0.017993 |
|
4 |
0.0375 |
0 |
0.041699 |
0.095158 |
0.013900 |
0.017820 |