Working with subgroups in variables control charts

A subgroup is a group of units that are created under the same set of conditions. Subgroups (or rational subgroups) represent a "snapshot" of the process. Therefore, the measurements within a subgroup must be taken close together in time but still be independent of each other.

For example, a die cut machine produces 100 plastic parts per hour. The quality engineer measures five randomly selected parts every hour. Each sample of five parts is a subgroup.

Choose subgroups so that differences between measurements within the same subgroup are small and so that you can detect differences between subgroups. For initial process studies, subgroups of 4 or 5 units that are collected every hour or so are common. As the process demonstrates stability (or as improvements are made), you can decrease the subgroup size and frequency.

Collect subgroups for a duration that is long enough to ensure that major sources of variation have the chance to occur. Usually, 100 observations or more (for example 25 subgroups with 4 observations each) is enough.

Usually, industry prefers small, frequent samples to signal a process shift before too much defective product is made.

A large total number of observations is clearly advantageous because you can learn more about process performance. However, a large subgroup size is not necessarily better. You have to consider the period of time in which these large numbers of observations are obtained. For example, if you choose the subgroup size as all the measurements taken on one day, any changes within a day might average each other out and remain undetected. The size of each subgroup should represent information about the inherent variation of the process (also called common-cause variation). If you know that few changes occur within a certain time interval, collect the subgroup data during that time period.

When collecting samples to learn about a process, it is usually best to combine the samples into subgroups.

When grouping is not appropriate, then a subgroup size of one provides a method for evaluating the process. Samples that cannot logically be grouped together are good candidates for individuals (I) and moving range (MR) charts.