XBar (xbar + sigma)
- Last UpdatedMar 19, 2016
- 3 minute read
The 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.
A chart point is the (xbar) value from each sample.
The examples given below illustrate the control limits calculated for chart point 0.94938.
|
Use Tables (sigma est = 0) |
|
|---|---|
|
Formula |
Example |
|
CL = Mean ( LCL = CL – (3 * ASTD) UCL = CL + (3 * ASTD) The adjusted standard deviation from the estimated standard deviation is ASTD. |
The estimated standard deviation is 0.02100 and the sample size obtained from the last sample is 4. CL = 0.95267 LCL = 0.95267 – (3 * 0.01050) = 0.92117 UCL = 0.95267 + (3 * 0.01050) = 0.98416 |
|
Use Std. Dev. (sigma est = 1) |
|
|---|---|
|
Formula |
Example |
|
CL = Mean ( LCL = CL – (3 * ASTD) UCL = CL + (3 * ASTD) The adjusted standard deviation from the calculated standard deviation is ASTD. |
The standard deviation calculated from the data is 0.02025 and the sample size obtained from the last sample is 4. CL = 0.95267 LCL = 0.95267 – (3 * 0.01013) = 0.92229 UCL = 0.95267 + (3 * 0.01013) = 0.98305 |
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) |
||||
|---|---|---|---|---|---|---|
|
LCL |
CL |
UCL |
Lower σ |
Upper σ |
||
|
1 |
0.949 |
0.924495 |
0.952667 |
0.980838 |
0.009391 |
0.009390 |
|
2 |
0.954167 |
0.916297 |
0.952667 |
0.989036 |
0.012123 |
0.012123 |
|
3 |
0.961667 |
0.916297 |
0.952667 |
0.989036 |
0.012123 |
0.012123 |
|
4 |
0.949375 |
0.921170 |
0.952667 |
0.984163 |
0.010499 |
0.010499 |
|
Label |
Chart Point |
Use Std. Dev. (sigma est = 1) |
||||
|---|---|---|---|---|---|---|
|
LCL |
CL |
UCL |
Lower σ |
Upper σ |
||
|
1 |
0.949 |
0.925493 |
0.952667 |
0.979841 |
0.009058 |
0.009058 |
|
2 |
0.954167 |
0.917585 |
0.952667 |
0.987748 |
0.011694 |
0.011694 |
|
3 |
0.961667 |
0.917585 |
0.952667 |
0.987748 |
0.011694 |
0.011694 |
|
4 |
0.949375 |
0.922285 |
0.952667 |
0.983048 |
0.010127 |
0.010127 |