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.
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)
size of subgroup i
weight of EWMA
parameter for Test 1. The default is 3.
1 J.M. Lucas and M.S. Saccucci (1990). "Exponentially Weighted Moving Average Control Schemes: Properties and Enhancements," Technometrics, 32, 1−12.