Definition of Rational Subgroup:

It’s so easy to misuse a control chart. But, if you understand that the data you collect for developing a control chart is dependent upon proper sampling, you will want to utilize the collection of rational subgroups.

Our discussion will cover what rational subgroups are, why it’s important to use them, and some helpful hints on developing a data sampling strategy to collect them.

## Overview: What is a rational subgroup?

The control chart represents the change in the process over time. The technique involves taking samples from the process, doing a few simple control limit calculations, and then plotting the values on the appropriate type of control.

The goal is to see if the *between-sample variation* signals common cause or special cause variation.

Your sampling technique can also introduce noise in your sample. That’s called *within-sample variation. *Your sampling strategy should minimize the *within-sample variation (noise)* so you can maximize your ability to see *between-sample variation (signal).*

The illustration below shows the impact of high within-sample variation on the ability to see between-sample variation.

The most common sampling strategies for ongoing process monitoring are periodic or systematic and a combination of periodic and rational subgrouping.

Note there is a time period between each unit selected to make up the subgroup. During that time period, operators, raw material lot, environmental conditions, and many other factors could have changed. This would increase the within sample variation, create noise and possibly mask your between sample variation.

But what if you selected consecutive units with a fixed time period between?

Assuming some velocity of this process, the consecutive units taken in a row would be the best way to achieve minimal within sample variation.

The odds are high that the units in your sample were made under the same conditions, thus eliminating any noise attributed to the within sample variation. If you saw a difference from Time 1 to Time 2, you can assume the variation was due to between sample variation or a change in the process. This type of sampling is referred to as rational subgrouping.

A rational subgroup has the following properties:

**From a reasonably homogeneous stable process:**Units within a sample subgroup are from a reasonably homogeneous stable process. If the time interval for forming your subgroups is too long and allows special cause variation to appear, or results in the inclusion of different process conditions, then your within variation may overshadow your between variation. This may prevent you from being able to see process change.**Independent:**Units within your subgroups are independent, meaning no unit influences or is influenced by another unit in your sample subgroup.**In time order:**Units must be in time order.

## 3 benefits of rational subgrouping

The minimization of within-sample variation, or noise, is accomplished through the process of rational subgrouping. That has many benefits; here are a few.

### 1. Improves your ability to see process change

The purpose of a control chart is to see change over time. That requires the ability to see sample-to-sample difference. Using rational subgroups accomplishes this by reducing within-sample variation.

### 2. Easy to capture data

You can reduce the time needed to capture a subgroup by taking consecutive units instead of repeatedly going back and grabbing another unit.

### 3. Measure of short-term variation

Within-sample variation is a measure of the short-term variation of your process. The use of rational subgrouping reduces the short-term variation by capturing data within a short interval of time.

## Why is a rational subgroup important to understand?

The basis for the proper use of a control chart is the management of within-sample variation. Understanding how rational subgroups accomplish this is important.

### Reduction of sampling noise

The goal of a control chart is to signal a process change over time. That signal can be masked if the samples you collected are noisy, meaning they have high within-sample variation. Rational subgroups will solve that problem.

### Use in Xbar and R charts

An Xbar control chart measures between-sample variation and is the signal as to whether your process has changed. The R chart measures the within-sample variation. If that isn’t in control, then the Xbar has little meaning. That’s why you look at and interpret the R chart before looking at the Xbar chart.

### Subgroup sample size

If you’re taking consecutive units to form a rational subgroup, how many should you take? Since you are assuming that all the items in your rational subgroup are reasonably homogeneous, you don’t need a large sample size. Often a number of 4 or 5 is used. Smaller, frequent samples are preferred to larger, infrequent samples.

## An industry example of rational subgrouping

Quality control (QC) technicians had a protocol for selecting items for display on a control chart. The manufacturing process consisted of long runs, and the key process metrics were continuous data.

The protocol was to grab a sample unit every 30 minutes until the QC tech had accumulated 5 units for his subgroup. Calculations were made, and the results posted on a Xbar/R control chart.

The manufacturing manager, Barry, had long complained that it seemed a process problem kept suddenly appearing based on the QC control chart. Gail, the Lean Six Sigma Black Belt assigned to work with Barry, questioned whether the sampling protocol was right.

After reviewing the protocol, Gail realized that capturing one sample every 30 minutes and creating a subgroup of 5 resulted in a high within-sample variation. Since the within-sample variation is used to construct the control limits for the Xbar/R chart, the resulting control limits were wider than they should be. The wider control limits reduced the sensitivity of the control chart to see changes in the process.

Everyone agreed that QC needed to start creating rational subgroups by consecutively collecting 5 units every hour. This reduced the within-sample variation, reduced the calculated width of the control limits, and increased the sensitivity of the Xbar chart. Barry was now able to be notified of a shifting process before things got bad.

## 3 best practices when thinking about rational subgroups

Rational subgroups are critical to the proper use of a control chart, so keep these few things in mind.

### 1. Properly define what is meant by *consecutive*

When it is feasible to collect actual consecutive units, then do it. In some situations, the units are being produced at too high a speed to physically grab 5 in a row. In those cases, grab the 5 as you can, and don’t worry if they aren’t actually consecutive. If the speed of the line is that fast, there is a good chance that the 5 you are able to capture will still be sufficiently homogeneous to be called a rational subgroup.

### 2. Use a consecutive and periodic strategy

Consecutive provides you the rational subgroup. Drawing these rational subgroups and using a fixed periodicity makes it easier to know when it’s time to sample. Something like 5 consecutive units every 30 minutes is a reasonable strategy depending on the specific nature of your process.

### 3. Be careful about artificially creating a rational subgroup

Sampling one unit every hour and claiming that you have a rational subgroup of 8 for the day is not correct and violates the notion of minimizing the within-sample variation.

## Frequently Asked Questions (FAQ) about rational subgroups

### 1. What are the characteristics of a rational subgroup?

- Units must be in time sequence.
- Units within the subgroup must be independent.
- Units must represent a single homogeneous process.

### 2. What is the purpose of a rational subgroup?

The purpose is to select sample items and form a subgroup with minimal within sample variation to distinguish and signal when the between-sample variation has changed.

### 3. Can I use rational subgrouping for ImR control charts

Since you are generating and collecting single data points, the concept of rational subgrouping doesn’t apply. One of the reasons for using an ImR chart is because the process changes so slowly, or only generates a single data point. This would invalidate the need for rational subgrouping. Rational subgrouping is geared for use with continuous data, where you are creating subgroups of individual units of more than 1.

## Is it rational to use rational subgroups?

Yes, it is. If you want your control chart to be sensitive to changes in your process, then creating rational subgroups is the way to go. The key is selecting items that minimize within sample variation. This is best accomplished by minimizing the time interval for collecting your subgroup. Consecutive items will do this.

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