Control Charts

Control charts are used to calculate control limits and estimate the process standard deviation. Control chart constants used are D4, D3, A2, and d2 (These control chart constants depend on the subgroup size n).

What are Control Chart Tables of Constants?

Control Chart Tables of Constants are values used for statistical process control. They provide reference points to determine if a process is in-control or out-of-control due to special causes. When control limits have been established, the constants A2, d2, D3 and D4 help to determine these limits and decide whether a process is stable or needs intervention to improve the quality of the product.

These control chart constants are summarised in the table below. For example, if your subgroup is 4, then D4 = 2.282, A2 = 0.729, and d2 = 2.059.

There is no value for D3. This simply means that the R chart has no lower control limit when the subgroup size is 4.

Knowing how to use Control Chart Tables of Constants – A2, d2, D3, and D4 – can greatly improve the quality control process. These tables provide useful reference points to determine whether a process is in-control or out-of-control. This guide will detail what each constant means and explore when and how it should be used.

Sub group Size (n) A2 D3 D4 d2
2 1.880   3.267 1.128
3 1.023   2.574 1.693
4 0.729   2.282 2.059
5 0.577   2.114 2.326
6 0.483   2.004 2.534
7 0.419 0.076 1.924 2.704
8 0.373 0.136 1.864 2.847
9 0.337 0.184 1.816 2.970
10 0.308 0.223 1.777 3.078
11 0.285 0.256 1.774 3.173
12 0.266 0.284 1.716 3.258
13 0.249 0.308 1.692 3.336
14 0.235 0.329 1.671 3.407
15 0.223 0.348 1.652 3.472
16 0.212 0.364 1.636 3.532
17 0.203 0.379 1.621 3.588
18 0.194 0.392 1.608 3.640
19 0.187 0.404 1.596 3.689
20 0.180 0.414 1.586 3.735
21 0.173 0.425 1.575 3.778
22 0.167 0.434 1.566 3.819
23 0.162 0.443 1.557 3.858
24 0.157 0.452 1.548 3.895
25 0.153 0.459 1.541 3.931