## 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?

This content shows the formulas for control limits for various Shewhart control charts. These formulas use an estimate of sigma. See Usage Note 36576 for information on how sigma is calculated for each chart.

**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 | ||||

Microsoft® Windows® 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 |