EWMA chart

To get started, the EWMA for subgroup 0 is set to the mean of all data. By changing the weight used and the number of σ's for the control limits, you can construct a chart with specific properties. Combinations of these two parameters are often chosen by using an ARL (average run length) table. See Lucas et al.¹ for the table of average run lengths.

Notation

Term	Description
r	weight
	mean of subgroup i

The center line represents the process average, μ. If you do not specify an historical value for μ, then Minitab uses the mean of all observations, , to estimate μ.

If you do not specify a historical value for the process standard deviation, σ, then Minitab estimates σ from your data using the specified method.

Standard deviation of the plotted points

For the first subgroup (), is calculated as follows:

For subsequent subgroups (), is calculated as follows:

When subgroup sizes are constant, the equation simplifies to the following:

Lower control limit (LCL)

Upper control limit (UCL)

Notation