A single subgroup tells you very little. To know what the process normally does, you need a history: 20 to 25 subgroups collected while the line ran under ordinary conditions. That history gives you the centrelines, the horizontal reference lines that the plotted points scatter around.
The centreline of the X̄ chart is the grand mean, written X̄̄ (X double-bar). It is the average of all the subgroup means. The centreline of the R chart is the average range, written R̄ (R-bar). It is the average of all the subgroup ranges. Both are simple averages; the only discipline is making sure the data came from a period when nothing unusual was happening.
If a subgroup in the baseline period came from a known upset, such as a jam that bent several flaps, leave it out and note why. Baseline data should describe the process as it runs when left alone, because the limits you calculate next will be judged against that picture.
Standard Procedure
- 1Collect at least 20 subgroups during normal running, recording X̄ and R for each.
- 2Remove any subgroup with a documented, explained upset.
- 3Add all subgroup means and divide by the number of subgroups to get X̄̄.
- 4Add all subgroup ranges and divide by the number of subgroups to get R̄.
- 5Draw both centrelines as solid horizontal lines on the chart.
Lesson Summary
- ✓X̄̄ and R̄ come from 20 to 25 subgroups collected under normal conditions.
- ✓A documented upset belongs out of the baseline, with a note explaining the exclusion.