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Table of Control Chart Constants
X-bar Chart for sigma R Chart Constants S Chart Constants
Constants estimate
Sample
Size = m
A
2
A
3
d
2
D
3
D
4
B
3
B
4
2
1.880
2.659
1.128
0
3.267
0
3.267
3
1.023
1.954
1.693
0
2.574
0
2.568
4
0.729
1.628
2.059
0
2.282
0
2.266
5
0.577
1.427
2.326
0
2.114
0
2.089
6
0.483
1.287
2.534
0
2.004
0.030
1.970
7
0.419
1.182
2.704
0.076
1.924
0.118
1.882
8
0.373
1.099
2.847
0.136
1.864
0.185
1.815
9
0.337
1.032
2.970
0.184
1.816
0.239
1.761
10
0.308
0.975
3.078
0.223
1.777
0.284
1.716
11
0.285
0.927
3.173
0.256
1.744
0.321
1.679
12
0.266
0.886
3.258
0.283
1.717
0.354
1.646
13
0.249
0.850
3.336
0.307
1.693
0.382
1.618
14
0.235
0.817
3.407
0.328
1.672
0.406
1.594
15
0.223
0.789
3.472
0.347
1.653
0.428
1.572
16
0.212
0.763
3.532
0.363
1.637
0.448
1.552
17
0.203
0.739
3.588
0.378
1.622
0.466
1.534
18
0.194
0.718
3.640
0.391
1.608
0.482
1.518
19
0.187
0.698
3.689
0.403
1.597
0.497
1.503
20
0.180
0.680
3.735
0.415
1.585
0.510
1.490
21
0.173
0.663
3.778
0.425
1.575
0.523
1.477
22
0.167
0.647
3.819
0.434
1.566
0.534
1.466
23
0.162
0.633
3.858
0.443
1.557
0.545
1.455
24
0.157
0.619
3.895
0.451
1.548
0.555
1.445
25
0.153
0.606
3.931
0.459
1.541
0.565
1.435
Control chart constants for X-bar, R, S, Individuals (called "X" or "I" charts), and MR (Moving Range) Charts.
NOTES: To construct the "X" and "MR" charts (these are companions) we compute the Moving Ranges as:
R
2
= range of 1st and 2nd observations, R
3
= range of 2nd and 3rd observations, R
4
= range of 3rd and 4th
observations, etc. with the "average" moving range or "MR-bar" being the average of these ranges with the
"sample size" for each of these ranges being n = 2 since each is based on consecutive observations ... this
should provide an estimated standard deviation (needed for the "I" chart) of
σ = (MR-bar)/d
2
where the value of d
2
is based on, as just stated, m = 2.
Similarly, the UCL and LCL for the MR chart will be: UCL = D
4
(MR-bar) and LCL = D
3
(MR-bar)
but, since D
3
= 0 when n = 0 (or, more accurately, is "not applicable") there will be no LCL for the MR chart,
just a UCL.