Rational Subgrouping is the name given to the way in which data are organized into subgroups for process control charts. Rational subgroups for process control charts involve the use of process and product knowledge and judgment, but there are a few basic principles that should be followed.

  •  Usually, the subgroups should be chosen so that within subgroup variation is minimized. For example, keep in mind that for an Average and Range chart, it is the within subgroup variation that determines how sensitive the chart will be since the average Range (R-bar) is used in the calculation of the Averages chart control limits
  • The selection of rational subgroups should be consistent with the structure of the data from the process
  • The selection of rational subgroups should allow for quick identification of potential corrective actions once an out-of-control condition is identified

Example: A process involves the filling of one-gallon cans of an expensive liquid using a machine with three filling heads. The operator has taken some initial data on the process and is trying to decide how to organize it into a process control chart. The initial data is given below. The characteristic being measured is fill volume (in gallons).

rational subgroup chart

The operator wants to obtain rational subgroups for the Average and Range chart but isn’t sure what that is. After consulting with a quality engineer, the following options emerge.

Option 1: Organize the data into subgroups of three taken each hour. The problem is that this approach will mix together the variation of the filling heads and make an out-of-control point on the average chart difficult to interpret.

Option 2: Organize the data by filling head utilizing an Individuals and Moving Range chart and plotting all three heads on the same chart. Again, this will be difficult to interpret. What will an out-of-control point mean? You would somehow need to identify each head on the chart.

Option 3: Treat each measure of each head as a rational subgroup of one and run three Individuals and Moving Range Charts (taking a measure from each head each hour). While this requires the use of three charts, it is the most productive organization of the data since it allows for quick interpretation of an out-of-control condition.