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

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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 JMP Note 575376 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_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:

[Previously JMP Note 36484]