How are control limits calculated for the different moving average control charts?

[#1]

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_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 E_i exceeds the limits.

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 μ₀ and σ₀ are available for μ and σ, respectively, replace

with μ₀ and

with σ₀ 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_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 A_i exceeds the limits.

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 μ₀ and σ₀ are available for μ and σ, respectively, replace

with μ₀ and replace

with σ₀ in the above formula. Note that the limits vary with both n_i and i.

[Previously JMP Note 36635]