Individual Values (ix)
- Last UpdatedMay 16, 2023
- 2 minute read
The LCL and UCL are calculated based on the sigma setting for a characteristic. The
tables below contain formulas to calculate the CL, LCL and UCL for a chart point.
Since the center line (CL) is the xbar (
), the center line, LCL and UCL is the same for all the chart points for this chart
type. A chart point is an individual reading (measurement data) collected for a characteristic.
The examples given below illustrate the control limits calculated for chart point 0.9350 (Sample ID: 51, ValueNumber:4).
|
Use Tables (sigma est = 0) |
|
|---|---|
|
Formula |
Example |
|
CL = Mean ( LCL = CL – (3 * Estimated Standard Deviation) UCL = CL + (3 * Estimated Standard Deviation) |
CL = 0.95267 LCL = 0.95267 – (3 * 0.02247) = 0.88526 UCL = 0.95267 + (3*0.02247) = 1.02008 For this example data, the estimated standard deviation is 0.02247. |
|
Use Std. Dev. (sigma est = 1) |
|
|---|---|
|
Formula |
Example |
|
CL = Mean ( LCL = CL – (3 * Standard Deviation) UCL = CL + (3 * Standard Deviation) |
CL = 0.95267 LCL = 0.95267 – (3 * 0.02025) = 0.89192 UCL = 0.95267 + (3 * 0.02025) = 1.01342 For this example data, the standard deviation is 0.02025. |
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 |
0.9100 |
0.885250 |
0.952667 |
1.020083 |
0.022472 |
0.022472 |
|
2 |
0.9550 |
0.885250 |
0.952667 |
1.020083 |
0.022472 |
0.022472 |
|
3 |
0.9800 |
0.885250 |
0.952667 |
1.020083 |
0.022472 |
0.022472 |
|
... |
||||||
|
15 |
0.9350 |
0.885250 |
0.952667 |
1.020083 |
0.022472 |
0.022472 |
|
Label |
Chart Point |
Use Std. Dev. (sigma est = 1) |
||||
|---|---|---|---|---|---|---|
|
LCL |
CL |
UCL |
Lower σ |
Upper σ |
||
|
1 |
0.9100 |
0.891904 |
0.952667 |
1.013430 |
0.020254 |
0.020254 |
|
2 |
0.9550 |
0.891904 |
0.952667 |
1.013430 |
0.020254 |
0.020254 |
|
3 |
0.9800 |
0.891904 |
0.952667 |
1.013430 |
0.020254 |
0.020254 |
|
... |
||||||
|
15 |
0.9350 |
0.891904 |
0.952667 |
1.013430 |
0.020254 |
0.020254 |