## Usage Note *36484: *How are control limits calculated for the different Shewhart control charts?

## How are control limits calculated for the different Shewhart control charts?

**Mean and Range Charts:**

You can compute the limits in the following ways:

- as a specified multiple (
*k*) of the standard errors of*X-bar*and_{i}*R*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
*X-bar*or_{i}*R*exceeds the limits._{i}

The following notation is used for the formulas:

The following tables provide the formulas for the limits:

**Mean and Standard Deviation Charts:**

You can compute the limits in the following ways:

- as a specified multiple (
*k*) of the standard errors of*X-bar*and_{i}*s*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
*X-bar*or_{i}*s*exceeds the limits._{i}

The following notation is used for the formulas:

The following tables provide the formulas for the limits:

**IR Charts:**

You can compute the limits in the following ways:

- as a specified multiple (
*k*) of the standard errors of*X*and_{i}*R*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
*X*or_{i}*R*exceeds the limits._{i}

The following notation is used for the formula:

The following tables provide the formulas for the limits:

**C Charts:**

You can compute the limits in the following ways:

- as a specified multiple (
*k*) of the standard error of*c*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
*c*exceeds the limits._{i}

The following notation is used for the formula:

The following equations give the formulas for the limits:

**NP Charts:**

You can compute the limits in the following ways:

- as a specified multiple (
*k*) of the standard error of*X*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
*X*exceeds the limits._{i}

The following notation is used for the formula:

The following equations give the formulas for the limits:

**P Charts:**

You can compute the limits in the following ways:

- as a specified multiple (
*k*) of the standard error of*p*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
*p*exceeds the limits._{i}

The notation for the p chart is the same as the notation for the np chart.

The following equations give the formulas for the limits:

**U Charts:**

You can compute the limits in the following ways:

- as a specified multiple (
*k*) of the standard error of*u*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
*u*exceeds the limits._{i}

The following notation is used for the formula:

The following equations give the formulas for the limits:

#### Operating System and Release Information

Product Family | Product | System | SAS Release | |

Reported | Fixed* | |||

JMP Software | JMP software | 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 Pro x64 | ||||

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

Microsoft Windows 8.1 Enterprise x64 | ||||

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: | 2009-09-17 10:10:08 |

Date Created: | 2009-07-09 11:49:32 |