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_i and R_i above and below the central line. The default limits are computed with k=3 (these are referred to as 3σ limits).
• as probability limits defined in terms of α, a specified probability that X-bar_i or R_i exceeds the limits.

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_i and s_i above and below the central line. The default limits are computed with k=3 (these are referred to as 3σ limits).
• as probability limits defined in terms of α, a specified probability that X-bar_i or s_i exceeds the limits.

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_i and R_i above and below the central line. The default limits are computed with k=3 (these are referred to as 3σ limits).
• as probability limits defined in terms of α, a specified probability that X_i or R_i exceeds the limits.

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_i above and below the central line. The default limits are computed with k=3 (these are referred to as 3σ limits).
• as probability limits defined in terms of α, a specified probability that c_i exceeds the limits.

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_i above and below the central line. The default limits are computed with k=3 (these are referred to as 3σ limits).
• as probability limits defined in terms of α, a specified probability that X_i exceeds the limits.

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_i above and below the central line. The default limits are computed with k=3 (these are referred to as 3σ limits).
• as probability limits defined in terms of α, a specified probability that p_i exceeds the limits.

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_i above and below the central line. The default limits are computed with k=3 (these are referred to as 3σ limits).
• as probability limits defined in terms of α, a specified probability that u_i exceeds the limits.

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.

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Type:	Usage Note
Priority:

Date Modified:	2009-09-17 10:10:08
Date Created:	2009-07-09 11:49:32