## Usage Note *36576: *How is the standard deviation calculated for different Shewhart control charts?

**XR Charts**

The estimate for σ is

where *N* is the number of subgroups for which
*n _{i}*>2, and

*R*is the sample range of the observations

_{i}*x*

_{i1},...,x_{in}in the*i*^{th}subgroup**XS Charts**

The estimate for σ is

where *N* is the number of subgroups for which
*n _{i}*>2, and

*s*is the sample standard deviation of the

_{i}*i*

^{th}subgroup

and

Here Γ(·) denotes the gamma function and

*X-bar*denotes the

_{i}*i*

^{th}subgroup mean.

**IR Charts**

The estimate for σ is

where *R-bar* is the average of the moving ranges, *n* is the
number of consecutive individual measurements used to
compute each moving range, and the unbiasing factor *d _{2}(n)* is
defined so that if the observations are normally distributed,
the expected value of

*R*is

_{i}#### Operating System and Release Information

Product Family | Product | System | SAS Release | |

Reported | Fixed* | |||

JMP Software | JMP software | Microsoft Windows 8.1 Pro 32-bit | ||

Microsoft Windows 8.1 Enterprise x64 | ||||

Microsoft Windows 8.1 Enterprise 32-bit | ||||

Microsoft Windows 8 Pro x64 | ||||

Microsoft Windows 8 Pro 32-bit | ||||

Microsoft Windows 8 Enterprise x64 | ||||

Microsoft Windows 8 Enterprise 32-bit | ||||

MicrosoftÂ® WindowsÂ® for x64 | ||||

Macintosh on x64 | ||||

Macintosh | ||||

Microsoft Windows 8.1 Pro x64 | ||||

Microsoft Windows 10 | ||||

Windows 7 Enterprise 32 bit | ||||

Windows 7 Enterprise x64 | ||||

Windows 7 Home Premium 32 bit | ||||

Windows 7 Home Premium x64 | ||||

Windows 7 Professional 32 bit | ||||

Windows 7 Professional x64 | ||||

Windows 7 Ultimate 32 bit | ||||

Windows 7 Ultimate x64 |

*****For software releases that are not yet generally available, the Fixed Release is the software release in which the problem is planned to be fixed.

Type: | Usage Note |

Priority: |

Date Modified: | 2009-07-21 20:00:55 |

Date Created: | 2009-07-20 14:06:23 |