Rational sub-grouping is the process of organizing the data into groups that were produced basically under the same conditions. In other words, it is a process to organize the data into groups that were produced under similar conditions to measure the variation between subgroups instead of each data point. 

Rational subgroups help in the estimation process of short-term variations. Thus, rational subgrouping is the basis for operating control charts in a successful manner. These variations later help us predict the long-term variations and their control limits, depending on the type of causes for the variation (special or common).

Rational subgroups indicate the common cause variation in the process and also the data collection method. For example, a plastic molding machine produces 200 bottles per hour. The supervisor randomly selects three bottles every hour and measures the weight in grams. The three bottles are one subgroup.

Types of variations

Within subgroup variation: Variation existed within subgroups, also known as inherent variation.

Between subgroup variation: Variation between the subgroups due to special causes in the process.

The control chart is a graph to study the process changes over time. A control chart always has a central line for the average, an upper line for the upper control limit, and a lower line for the lower control limit. The control limits are ±3σ from the centerline. The control limits are computed using the variation of subgroups. Thus, it is important to select subgroups that have only inherent variation. The most effective way to improve process quality is by finding a way to achieve minimum variation within and between the subgroups.

Rational subgroup best practices

• The subgroups are all formed from the observations that have been taken in a sequence (time-ordered).
• Select the subgroups to make each subgroup as homogeneous as possible. This provides the maximum opportunity for estimating expected variation from one subgroup to another.
• The observations within the subgroups are independent, which means no observation influences, or results from, another.
• The observations within a subgroup come from a lone steady process. Otherwise, the special causes that occur at high frequency within the subgroup result in high variation between the subgroups.

When do we need Rational Subgroups?

• Special cause variation in the process may divulge the need for rational subgrouping.
• Non-normal data can sometimes also indicate sub-groups exist.

Steps to Develop Rational Subgroups

• Identify the right data (Quality characteristics that are important to customers) to capture or track.
• Select the source of data and the categories like shift, material, machine, etc. 
• Produce elements of the subgroup in closely similar identical ways and determine the range of variation within the subgroup.
• Select the best sample data for subgrouping to get the desired control chart.
• Use the ANOVA test to confirm the statistical difference between sub-groups.

Example of Rational Subgroup

Example: There are four bottle-filling machines in XYZ Inc. The amount of material filling each bottle is one of the critical quality characteristics that we are looking to monitor. Below are the different methods of subgrouping the data for the control chart.

Step 1: The first subgroup consists of four bottles from machine 1. The second subgroup consists of four bottles from machine 2, and the third subgroup consists of four bottles from machine 3. Finally, the fourth subgroup consists of four bottles from machine 4.

Step 2: Form a subgroup consisting of one bottle each from four machines.

Step 3: Select each subgroup to have a mix of four bottles from the machines.

Compute the Range chart, standard deviation, and average chart for all the above three scenarios and determine the best subgrouping method.

Rational subgroups of individual control charts

Often rational subgrouping is a little bit unclear when dealing with individual control charts. In other words, when the subgroup size is one. The basic idea underlying control charts of all types is to identify the capability of the process. The mechanism by which this is accomplished is the careful formation of rational subgroups.

Additional Rational Sub Grouping Resources

• https://qualityamerica.com/LSS-Knowledge-Center/statisticalprocesscontrol/rational_subgroups.php
• https://www.moresteam.com/university/workbook/wb_subgroupintro.pdf

Subgrouping Video