Quality Advisor
A free online reference for statistical process control, process capability analysis, measurement systems analysis, and control chart interpretation, and other quality metrics.
X-bar and range chart formulas
X-bar control limits are based on either range or sigma, depending on which chart it is paired with. When the X-bar chart is paired with a range chart, the most common (and recommended) method of computing control limits based on 3
standard deviations 
is:
X-bar
n is the number of observations
|
k is the number of subgroups
|
| Upper control limit:
|
Lower control limit:
 |
Range
 |
k is the number of subgroups.
|
Upper control limit:
 |
Lower control limit:
 |
Subgroup Size |
A2 |
d2 |
D3 |
D4 |
2 |
1.880 |
1.128 |
----- |
3.268 |
3 |
1.023 |
1.693 |
----- |
2.574 |
4 |
0.729 |
2.059 |
----- |
2.282 |
5 |
0.577 |
2.326 |
----- |
2.114 |
6 |
0.483 |
2.534 |
----- |
2.004 |
7 |
0.419 |
2.704 |
0.076 |
1.924 |
8 |
0.373 |
2.847 |
0.136 |
1.864 |
9 |
0.337 |
2.970 |
0.184 |
1.816 |
10 |
0.308 |
3.078 |
0.223 |
1.777 |
11 |
0.285 |
3.173 |
0.256 |
1.744 |
12 |
0.266 |
3.258 |
0.283 |
1.717 |
13 |
0.249 |
3.336 |
0.307 |
1.693 |
14 |
0.235 |
3.407 |
0.328 |
1.672 |
15 |
0.223 |
3.472 |
0.347 |
1.653 |
16 |
0.212 |
3.532 |
0.363 |
1.637 |
17 |
0.203 |
3.588 |
0.378 |
1.622 |
18 |
0.194 |
3.640 |
0.391 |
1.608 |
19 |
0.187 |
3.689 |
0.403 |
1.597 |
20 |
0.180 |
3.735 |
0.415 |
1.585 |
21 |
0.173 |
3.778 |
0.425 |
1.575 |
22 |
0.167 |
3.819 |
0.434 |
1.566 |
23 |
0.162 |
3.858 |
0.443 |
1.557 |
24 |
0.157 |
3.895 |
0.451 |
1.548 |
25 |
0.153 |
3.931 |
0.459 |
1.541 |
|
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