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A free online reference for statistical process control, process capability analysis, measurement systems analysis, control chart interpretation, and other quality metrics.

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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

x-bar formula
n is the number of observations

x-double bar formula
k is the number of subgroups

Upper control limit:

x-bar & range upper control limit formula

Lower control limit:

x-bar & range lower control limit formula

Range

range formula r-bar formula
k is the number of subgroups.

Upper control limit:

range chart upper control limit formula

Lower control limit:

range chart lower control limit formula


Tabular values for X-bar and range charts
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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