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

## 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 | Macintosh | ||

Microsoft Windows XP 64-bit Edition | ||||

MicrosoftÂ® WindowsÂ® for x64 | ||||

Microsoft Windows 2000 Server | ||||

Microsoft Windows 2000 Professional | ||||

Microsoft Windows Server 2003 Standard Edition | ||||

Microsoft Windows Server 2008 | ||||

Microsoft Windows XP Professional | ||||

Windows Vista | ||||

Linux | ||||

Linux for 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 |