Control Charts
Control Chart Constants Table
A2, A3, B3, B4, D3, D4, d2, d3, c4 — all constants for subgroup sizes n = 2 to 25. Source: AIAG SPC Manual.
Quick Lookup — click a row to highlight
Control Limit Formulas
X̄-R Chart
UCL = X̄ + A₂R̄
LCL = X̄ − A₂R̄
Uses: A2
X̄-S Chart
UCL = X̄ + A₃S̄
LCL = X̄ − A₃S̄
Uses: A3
R Chart
UCL = D₄R̄
LCL = D₃R̄
Uses: D3, D4
S Chart
UCL = B₄S̄
LCL = B₃S̄
Uses: B3, B4
Complete Constants Table
| n | d2 | d3 | c4 | A2 | A3 | D3 | D4 | B3 | B4 |
|---|---|---|---|---|---|---|---|---|---|
| 2 | 1.128 | 0.853 | 0.7979 | 1.880 | 2.659 | 0.000 | 3.267 | 0.000 | 3.267 |
| 3 | 1.693 | 0.888 | 0.8862 | 1.023 | 1.954 | 0.000 | 2.575 | 0.000 | 2.568 |
| 4 | 2.059 | 0.880 | 0.9213 | 0.729 | 1.628 | 0.000 | 2.282 | 0.000 | 2.266 |
| 5 | 2.326 | 0.864 | 0.9400 | 0.577 | 1.427 | 0.000 | 2.115 | 0.000 | 2.089 |
| 6 | 2.534 | 0.848 | 0.9515 | 0.483 | 1.287 | 0.000 | 2.004 | 0.030 | 1.970 |
| 7 | 2.704 | 0.833 | 0.9594 | 0.419 | 1.182 | 0.076 | 1.924 | 0.118 | 1.882 |
| 8 | 2.847 | 0.820 | 0.9650 | 0.373 | 1.099 | 0.136 | 1.864 | 0.185 | 1.815 |
| 9 | 2.970 | 0.808 | 0.9693 | 0.337 | 1.032 | 0.184 | 1.816 | 0.239 | 1.761 |
| 10 | 3.078 | 0.797 | 0.9727 | 0.308 | 0.975 | 0.223 | 1.777 | 0.284 | 1.716 |
| 11 | 3.173 | 0.787 | 0.9754 | 0.285 | 0.927 | 0.256 | 1.744 | 0.321 | 1.679 |
| 12 | 3.258 | 0.778 | 0.9776 | 0.266 | 0.886 | 0.284 | 1.716 | 0.354 | 1.646 |
| 13 | 3.336 | 0.770 | 0.9794 | 0.249 | 0.850 | 0.308 | 1.692 | 0.382 | 1.618 |
| 14 | 3.407 | 0.763 | 0.9810 | 0.235 | 0.817 | 0.329 | 1.671 | 0.406 | 1.594 |
| 15 | 3.472 | 0.756 | 0.9823 | 0.223 | 0.789 | 0.348 | 1.652 | 0.428 | 1.572 |
| 20 | 3.735 | 0.729 | 0.9869 | 0.180 | 0.680 | 0.415 | 1.585 | 0.510 | 1.490 |
| 25 | 3.931 | 0.708 | 0.9896 | 0.153 | 0.606 | 0.459 | 1.541 | 0.565 | 1.435 |
D3 = 0 for n ≤ 6 (lower control limit not applicable for small subgroups).