A control chart is a running picture of a process over time. The X̄-R chart (say "X-bar R") is the most common version for measured values such as a length or a thickness. It uses two plots stacked together: the top one tracks where the process is centred, and the bottom one tracks how much it spreads.
The raw material for the chart is the subgroup. A subgroup is a small set of pieces, usually 3 to 5, taken close together in time. On a carton converting line, that might be five cartons pulled one after another at the top of every hour. Taking them consecutively matters: five pieces made within a minute show the natural short-term wobble of the machine, not the drift between shifts.
For each subgroup you calculate two numbers. X̄ is the subgroup mean, the plain average of the five readings. R is the range, the largest reading minus the smallest. X̄ feeds the top chart and R feeds the bottom chart. Nothing more complicated than adding, dividing, and subtracting is needed at this stage.
Standard Procedure
- 1Decide the subgroup size (5 is common) and the sampling interval (every hour on this line).
- 2Pull the pieces consecutively from the same machine, not spread across the shift.
- 3Measure each piece with the same gauge and record all readings on the chart form.
- 4Add the readings and divide by the subgroup size to get X̄.
- 5Subtract the smallest reading from the largest to get R, then plot both points.
Lesson Summary
- ✓X̄ is the average of one subgroup; R is its largest reading minus its smallest.
- ✓Consecutive pieces capture short-term, common-cause variation, which is what the chart needs to measure.