Statistical Process Control and Data Analytics, 8th Edition

Appendix DConstants used in the design of control charts for median and range

Sample size (n)	Constants for median charts		Constants for range(R) The difference between the largest and the smallest result in a sample of individuals – an approximate and easy measure of the degree of scatter. charts
	A4	$2/3A_4$	$D_{.001}^{\text{m}}$	$D_{.001}^{\text{m}}$
2	2.22	1.48	3.98	2.53
3	1.27	0.84	2.83	1.79
4	0.83	0.55	2.45	1.55
5	0.71	0.47	2.24	1.42
6	0.56	0.37	2.12	1.34
7	0.52	0.35	2.03	1.29
8	0.44	0.29	1.96	1.24
9	0.42	0.28	1.91	1.21
10	0.37	0.25	1.88	1.18

Formulae

$\begin{array}{cccc}Medianchart\hfill & \text{Action lines}\hfill & =& \tilde{\tilde{X}}\pm A_4\tilde{R}\hfill \\ \text{Upper}\text{lines}\hfill & =& \tilde{\tilde{X}}\pm 2/3A_4\tilde{R}\hfill \\ Rangechart\hfill & \text{Upper}\text{ action}\text{lines}\hfill & =& D_{.001}^{\text{m}}\tilde{R}\hfill \\ \text{Upper}\text{ warning}\text{lines}\hfill & =& D_{.025}^{\text{m}}\tilde{R}\hfill \end{array}$