## Usage Note *36635: *How are control limits calculated for the different moving average control charts?

**EWMA Charts:**

The following notation is used for the formulas:

You can compute the limits in the following ways:

- as a specified multiple (
*k*) of the standard error of*E*above and below the central line. The default limits are computed with_{i}*k=3*(these are referred to as 3σ*limits*). - as probability limits defined in terms of α, a specified probability that
*E*exceeds the limits._{i}

The following table presents the formulas for the control limits:

The following table presents the formulas for the probability limits:

These formulas assume that the data are normally distributed. If standard values μ_{0} and σ_{0}
are available for μ and σ, respectively, replace _{
}
with μ_{0} and _{
}
with σ_{0} in the above formula. Note that the limits vary with both *n _{i}*
and

*i*.

**UWMA Charts:**

The following notation is used for the formulas:

You can compute the limits in the following ways:

- as a specified multiple (
*k*) of the standard error of*A*above and below the central line. The default limits are computed with_{i}*k=3*(these are referred to as 3σ*limits*). - as probability limits defined in terms of α, a specified probability that
*A*exceeds the limits._{i}

The following table presents the formulas for the control limits:

The following table presents the formulas for the probability limits:

These formulas assume that the data are normally distributed. If standard values μ_{0} and σ_{0}
are available for μ and σ, respectively, replace _{ }
with μ_{0} and replace _{
}
with σ_{0} in the above formula. Note that the limits vary with both *n _{i}*
and

*i*.

#### Operating System and Release Information

Product Family | Product | System | SAS Release | |

Reported | Fixed* | |||

JMP Software | JMP software | 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 32-bit | ||||

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: | 2009-07-29 09:18:44 |

Date Created: | 2009-07-27 14:57:30 |