# X-bar and sigma

## What is it?

An X-bar and s (sigma) chart is a special purpose variation of the X-bar and R chart. Used with processes that have a subgroup size of 11 or more, X-bar and s charts show if the system is stable and predictable. They are also used to monitor the effects of process improvement theories. Instead of using subgroup range to chart variability, these charts use subgroup standard deviation. Because standard deviation uses each individual reading to calculate variability, it provides a more effective measure of the process spread. X-bar and sigma charts To create an X-bar and sigma chart using software, download a copy of SQCpack.

## What does it look like?

The X-bar chart, on top, shows the mean or average of each subgroup. It is used to analyze central location. The sigma chart, on the bottom, shows how the data is spread and used to study system variability.

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## When is it used?

Use the X-bar and s charts to analyze variables data with subgroups of 11 or more or when you want the most efficient measure of subgroup variability.

Use X-bar and s charts when you can answer yes to these questions:

1. Do you need to assess system stability?

2. Is the data in variables form?

3. Is the data collected in subgroups larger than ten?

4. Is the time order of subgroups preserved?

## Getting the most

Collect as many subgroups as possible before calculating control limits. With smaller amounts of data, the X-bar and s chart may not represent the variability of the entire system. The more subgroups you use in control limit calculations, the more reliable the analysis. Typically, 20 to 25 subgroups will be used in control limit calculations.

X-bar and s charts have several applications. When you begin improving a system, use them to assess the system’s stability .

After the stability has been assessed, determine if you need to stratify the data. You may find entirely different results between shifts, among workers, among different machines, among lots of materials, etc. To see if variability on the X-bar and s chart is caused by these factors, you should collect and enter data in a way that lets you stratify by time, location, symptom, operator, and lots.

You can also use X-bar and s charts to analyze the results of process improvements. Here you would consider how the process is running and compare it to how it ran in the past. Do process changes produce the desired improvement?

Finally, use X-bar and s charts for standardization. This means you should continue collecting and analyzing data throughout the process operation. If you made changes to the system and stopped collecting data, you would have only perception and opinion to tell you whether the changes actually improved the system. Without a control chart, there is no way to know if the process has changed or to identify sources of process variability.