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.
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.
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:
Term | Description |
---|---|
n_{i} | size of subgroup i |
r | weight of EWMA |
μ | process mean |
k | parameter for Test 1. The default is 3. |