When you speak of subgrouping, it is usually in the context of constructing a control chart. Let’s explore the topic in a little more detail.

Subgrouping is a technique used in control charts to group data into smaller, more manageable sets or subgroups. The purpose of subgrouping is to increase the sensitivity of the control chart to detect small shifts or changes in the process.

The concept of subgrouping for control charts was first introduced by Walter A. Shewhart in the 1920s. Shewhart is widely considered to be the father of statistical process control (SPC) and is credited with developing the first control chart while working at the Western Electric Company’s Hawthorne Works in Cicero, Illinois. Shewhart’s work on SPC laid the foundation for modern quality control methods and had a profound impact on manufacturing and other industries.

In general, a control chart is used to monitor a process over time by plotting data points on a chart and analyzing the pattern of variation. The data points are typically collected in consecutive order and plotted in a time series. However, collecting data one point at a time may result in a chart that is too variable to be useful.

## Overview: What is subgrouping?

In general, a control chart is used to monitor a process over time by plotting data points on a chart and analyzing the pattern of variation. The data points are typically collected in consecutive order and plotted in a time series. However, collecting data one point at a time may result in a chart that is too variable to be useful.

By grouping the data into subgroups, you can reduce the variability within each subgroup and increase the ability of the control chart to detect meaningful changes in the process. In other words, by properly using subgroups, you will minimize the within-sample variation thereby increasing the ability to spot between sample variation. Subgrouping also allows you to calculate subgroup statistics, such as the subgroup mean and range, which can be used to calculate control limits and monitor the process performance.

The most common method of subgrouping is to group the data into consecutive, non-overlapping time periods of a fixed size. For example, you might collect data in subgroups of five consecutive data points, or ten consecutive data points. You might do that every shift or every hour. The choice of subgrouping method will depend on the specific characteristics of the process being monitored and the goals of the analysis. The key to forming a subgroup is to try and maximize the homogeneity of the subgroup. Selecting consecutive data points will allow this to happen.

## An industry example of subgrouping

A beverage manufacturer wanted to monitor their fill line to assure there is a consistent fill level for their product. The production line moves at a fast pace and is prone to some variation. The company’s Six Sigma Black Belt (BB) decided to use an Xbar and R control chart. Since he wanted the ability to quickly spot any change in the process, he decided to select subgroups of size 5 every hour on the hour to monitor the variation of the process. He used his first 20 subgroups to do the calculations and construct the chart. Below is the control chart he developed for fill level. As  you can see, the process appears to be in-control and exhibiting common cause variation.

Here are some frequently asked questions about subgrouping in statistical process control:

### What is the purpose of subgrouping in control charts?

The purpose of subgrouping is to reduce the variability within each subgroup and increase the sensitivity of the control chart to detect small shifts or changes in the process. Subgrouping also allows us to calculate subgroup statistics, such as the subgroup mean and range, which can be used to calculate control limits and monitor the process performance.

### What are some common methods of subgrouping?

The most common method of subgrouping is to group the data into consecutive, non-overlapping time periods of a fixed size. For example, you might collect data in subgroups of five consecutive data points, or ten consecutive data points.

### How do you choose the subgroup size?

The choice of subgroup size will depend on the specific characteristics of the process being monitored and the goals of the analysis. A larger subgroup size will result in a chart with less variability but with reduced sensitivity to detect small shifts. A smaller subgroup size will increase the sensitivity of the chart but may result in a chart with more variability. Generally, a subgroup size of 4 to 7 is recommended. Smaller and more frequent subgroups are better than larger and less frequent ones.

### What is the difference between within-subgroup variation and between-subgroup variation?

Within-subgroup variation refers to the variation within each subgroup, while between-subgroup variation refers to the variation between subgroups. In control chart analysis, you are interested in reducing the within-subgroup variation to increase the sensitivity of the chart to detect small shifts in the process. However, we also need to monitor the between-subgroup variation to ensure that the process is stable over time.