## Usage Note *35442: *How is the standard deviation calculated for the different moving average control charts in JMP®?

**EWMA and UWMA Charts**

The estimate for σ is

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

*s*is the standard deviation of the

_{i}*i*subgroup

^{th}and

Here denotes the gamma function and denotes the

*i*subgroup mean. A subgroup standard deviation

^{th}*s*is included in the claculation only if

_{i}*n*≥2. If the observations are normally distributed, then the expected value of

_{i}*s*is

_{i}*c*. Thus, is the unweighted average of

_{4}(n_{i})σ*N*unbiased estimates of σ.

When each subgroup sample contains a single observation (*n _{i}*=1), the process standard deviation σ is estimated as

where

*N*is the number of observations and

*x*are the individual measurements.

_{i},x_{2},...,x_{n}#### 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 | ||||

Microsoft® Windows® 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: | 2009-04-02 15:06:20 |

Date Created: | 2009-04-02 14:24:27 |