# X Bar/Range Control Charts For Data Collected by Subgroup Sampling

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## A Word About Control Charts

The individuals chart is the most basic type of control chart and in many cases provides sufficient information to understand the special cause and common cause variation in a process. With some types of data, however, a specialized control chart is preferable. Learn more about these types in these articles:

For data obtained by subgroup sampling, the best control chart is the X-bar/R (x-bar and range) chart.

## Using X-Bar/Range (X-Bar/R) Control Charts

An X-bar/R chart is actually two control charts in one: a chart of the average (X-bar) over time, plus a chart of the range (R) over time. This type of chart is helpful when you are analyzing a sample of continuous data and have reason to believe that data gathered within a short time frame would show less variation than data over a longer period.

In such a situation, the data for the control chart is obtained using subgroup sampling, which involves grouping together data obtained under identical or nearly identical conditions. This is often the case in manufacturing settings, where the conditions on an assembly line may vary over time but are generally constant within a short time period.

Employees may gather data by examining or measuring a sample of items processed within a single shift to create a subgroup. Each data point on the control chart then represents one sample or subgroup, and the data is said to be grouped into “rational subgroups.” Note that each observation should be independent, meaning it is not influenced by the other observations. This assumption would not hold for data such as hold times on a customer support phone line or wait times in a bank teller line.

If the subgroups are correctly implemented, the variation within a subgroup (short-term variation) should be minimal relative to the variation between subgroups (long-term variation). The R control chart tells you if any special cause exists in your range data, in the form of outliers (points outside the control limits) or trends. If the range data is in control (shows no special cause), you can then analyze the averages for special cause using the X-bar control chart.

By using an X-bar/R chart you can distinguish changes in process variability from changes in process average. Both are important elements of process performance, but the corrective actions vary depending on which type of change is occurring. A software program like Minitab makes creating these more involved charts simple.

Most experts recommend that the X-bar and range chart be used only when the sample size is fairly small, usually no larger than 10 or 15 observations per sample. When the subgroups are larger, a better control chart is the X-bar/S chart, which uses the standard deviation rather than the moving range as the measure of variation within subgroups. As with any control charts, you should run a normality test on the data to ensure that it meets that requirement.

Resource

National Institute of Standards and Technology: Shewhart X-bar and R and S Control Charts

## This post is part of the series: Types of Control Charts

Control charts are a powerful tool for Six Sigma projects, allowing analysis of special cause and common cause process variation. Learn about the different types and their uses.