## Estimates of Standard Deviation Based on Control Charts

From Chuck:

Control chart estimates of the standard deviation depend on the control chart used and the subgroup size. In each case, the estimated standard deviation is calculated as the average subgroup variation divided by a constant which is a function of the subgroup size. The following table contains the control chart estimated standard deviation calculations.

Chart Type | Symbol | Sub Size | Formula | Comments
XMR(2) | `S_(XMR2)` | 2 | `(MRBar)/(d2(2))` | MRBar is the average moving range.
XMR(3) | `S_(XMR3)` | 3 | `(MRBar)/(d2(3))` | MRBar is the average moving range.
RX | `S_(RX)` | 2 | `(PRBar)/(d2(2))` | PRBar is the average paired range.
XBar&R | `S_(XBR)` | m | `(RBar)/(d2(m))` | RBar is the average subgroup range. Subgroup size is m.
XBar&S | `S_(XBS)` | m | `(SBar)/(c4(m))` | SRBar is the average subgroup standard deviation. Subgroup size is m.
XTilde&R | `S_(XTR)` | m | `(RBar)/(d2(m))` | MRBar is the average subgroup range. Subgroup size is m.