### Estimates of Standard Deviation Based on Control Charts

The following calculations of estimated standard deviation are used in the calculation of capability indices for control charts:

Sigma Based on the Range:

`Sigm\a_((R))=barR/d_2`
where `barR` is the average subgroup range from the XBar & R or X Tilde & R Chart and `d_2` is the standard SPC constant based on the subgroup size.

Sigma Based on the Subgroup Standard Deviation:

`Sigm\a_((S))=barS/c_4`
where `barS` is the average subgroup standard deviation from the XBar & S Chart and `c_4` is the standard SPC constant based on the subgroup size.

Sigma Based on the Paired Range:

`Sigm\a_((PR))=bar(PR)/d_2`
where `bar(PR)` is the average subgroup range from the RX Chart and `d_2` is the standard SPC constant using subgroup size 2.

Sigma Based on the Moving Range:

`Sigm\a_((MR2))=bar(MR)/d_2`
where `bar(MR)` is the average subgroup range from the XMR(2) Chart and `d_2` is the standard SPC constant using subgroup size 2.

`Sigm\a_((MR3))=bar(MR)/d_2`
where `bar(MR)` is the average subgroup range from the XMR(3) Chart and `d_2` is the standard SPC constant using subgroup size 3.

See also:

Capability Indexes: Table of Calculations