Control Chart Constants Table (A2, D3, D4, d2, c4)

Constants for subgroup sizes 2–25

d2 and d3 are the AIAG / ASTM E2587 table values; c4 is computed exactly; the remaining factors are derived from them, which is how SpcLite computes control limits.

n	A2	A3	B3	B4	D3	D4	d2	d3	c4
2	1.8806	2.6587	0.0000	3.2665	0.0000	3.2686	1.1280	0.8530	0.7979
3	1.0231	1.9544	0.0000	2.5682	0.0000	2.5735	1.6930	0.8880	0.8862
4	0.7285	1.6281	0.0000	2.2660	0.0000	2.2822	2.0590	0.8800	0.9213
5	0.5768	1.4273	0.0000	2.0890	0.0000	2.1144	2.3260	0.8640	0.9400
6	0.4833	1.2871	0.0304	1.9696	0.0000	2.0039	2.5340	0.8480	0.9515
7	0.4193	1.1819	0.1177	1.8823	0.0758	1.9242	2.7040	0.8330	0.9594
8	0.3726	1.0991	0.1851	1.8149	0.1359	1.8641	2.8470	0.8200	0.9650
9	0.3367	1.0317	0.2391	1.7609	0.1838	1.8162	2.9700	0.8080	0.9693
10	0.3082	0.9754	0.2837	1.7163	0.2232	1.7768	3.0780	0.7970	0.9727
11	0.2851	0.9274	0.3213	1.6787	0.2559	1.7441	3.1730	0.7870	0.9754
12	0.2658	0.8859	0.3535	1.6465	0.2836	1.7164	3.2580	0.7780	0.9776
13	0.2494	0.8495	0.3816	1.6184	0.3076	1.6924	3.3360	0.7700	0.9794
14	0.2353	0.8173	0.4062	1.5938	0.3281	1.6719	3.4070	0.7630	0.9810
15	0.2231	0.7885	0.4282	1.5718	0.3468	1.6532	3.4720	0.7560	0.9823
16	0.2123	0.7626	0.4479	1.5521	0.3630	1.6370	3.5320	0.7500	0.9835
17	0.2028	0.7391	0.4657	1.5343	0.3779	1.6221	3.5880	0.7440	0.9845
18	0.1943	0.7176	0.4818	1.5182	0.3909	1.6091	3.6400	0.7390	0.9854
19	0.1866	0.6979	0.4966	1.5034	0.4031	1.5969	3.6890	0.7340	0.9862
20	0.1796	0.6797	0.5102	1.4898	0.4145	1.5855	3.7350	0.7290	0.9869
21	0.1733	0.6629	0.5228	1.4772	0.4251	1.5749	3.7780	0.7240	0.9876
22	0.1675	0.6473	0.5344	1.4656	0.4344	1.5656	3.8190	0.7200	0.9882
23	0.1621	0.6327	0.5452	1.4548	0.4432	1.5568	3.8580	0.7160	0.9887
24	0.1572	0.6191	0.5553	1.4447	0.4516	1.5484	3.8950	0.7120	0.9892
25	0.1526	0.6063	0.5648	1.4352	0.4597	1.5403	3.9310	0.7080	0.9896

Xbar-R chart formulas

Xbar chart: UCL = X̿ + A2·R̄, CL = X̿, LCL = X̿ − A2·R̄
R chart: UCL = D4·R̄, CL = R̄, LCL = D3·R̄
Within-subgroup σ: σ̂ = R̄ / d2

Xbar-S chart formulas

Xbar chart: UCL = X̿ + A3·S̄, LCL = X̿ − A3·S̄
S chart: UCL = B4·S̄, CL = S̄, LCL = B3·S̄
Within-subgroup σ: σ̂ = S̄ / c4 — prefer Xbar-S over Xbar-R when n > 8

I-MR chart formulas

Individuals charts use moving ranges of two consecutive points, so the n = 2 constants apply.

I chart: UCL = X̄ + 3·MR̄/1.128 (equivalently X̄ ± 2.66·MR̄)
MR chart: UCL = 3.267·MR̄, LCL = 0

Skip the hand calculation

Paste your data into SpcLite and it computes the limits, flags points with the eight tests for special causes, and runs capability on the same column.

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