# Xbar and Range (Xbar-R) Chart

Learn how to use this combined view to track variation across across a single characteristic—and pinpoint issues at a glance.

## What are the Components of the Xbar and Range Chart?

The Xbar chart—the upper section in this statistical process control (SPC) chart—plots the average of individual values in a subgroup (i.e., the subgroup mean). The Range chart (R)—(the lower section in the chart— plots the difference (or range) between the maximum and minimum individual values within the subgroup.

### Xbar-R Charts for a Single Characteristic

An Xbar-R chart is a quality control chart used to plot subgroup means and ranges of individual values from a single characteristic on a given part that were all produced on the same machine. A traditional Xbar-R chart is a single stream of data for a unique Part/Process/Test combination.

For example, this chart (taken from InfinityQS® ProFicient™ software) shows 20 subgroups. The highlighted section shows that both the average and range plot points for subgroup 8 are well within control limits. Judging from the control chart as a whole, this process is consistent (no plot points fall outside control limits) and only common cause variation is present.

Scroll down to learn how to use this chart.

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## When to Use the Xbar-R Chart

Use the Xbar-R chart when the sample size is between 2 and 9 (typically 3 or 5). This chart is often used when at least a few parts are made every hour and you can collect data at a reasonable cost.

The special use examples discussed for this chart all deal with sample sizes between 2 and 9.

• Easy to read and understand
• Widely recognized; operates on principles that serve as the foundation for more advanced control charts
• Separates variation in averages from variation in standard deviation
• Must use a separate chart for each characteristic
• Only two values per subgroup are used to estimate the standard deviation for the range, regardless of sample size
• Cannot be used to accurately indicate process variability for sample sizes greater than 9

## Decision Tree

Use the following decision tree to determine whether the Xbar-R chart is the best choice.
Scroll down to see special use examples.

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Control charts are invaluable for manufacturing optimization. But many manufacturers continue to rely on manual data management methods that are time consuming, frustrating, and vulnerable to inaccuracies.

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## Special Uses

Today, control charts are a key tool for quality control and figure prominently in Lean manufacturing and Six Sigma efforts.

### Target Xbar-R Chart

Target Xbar-R charts can help you identify changes in the average and range of averages of a characteristic. You can measure the characteristic across part numbers, but each part number must form a separate subgroup because target values change with the part number. Set the target values at the desired center, typically the center two-sided specifications.

• Plot multiple parts, characteristics, or specs on the same chart, as long as variability is similar across all parts, characteristics, or specifications.
• Plot data from gauges that are zeroed out on target values without needing to code or transform the data.
• Assess statistical control for both the part (or characteristic) and the process.

### Short Run Xbar-R Chart

Short run charts are used for short production runs. The short run Xbar-R chart can help you identify changes in the averages and range of averages of multiple characteristics, even those with different nominals, units of measure, or standard deviations.

• Use one chart to detect variations across multiple process or product characteristics, even for parts that have different means, units of measure, or standard deviation.
• Identify characteristics that should be prioritized for attention.
• Easily separate process- and product-specific variations as well as variations that are caused by changes in a subgroup mean and those that are caused by changes in the standard deviation.

### Group Xbar-R Chart

Group Xbar-R charts help you assess changes in averages and the range of averages across measurement subgroups for a characteristic.

• Easily identify characteristics that need priority attention.
• Easily separate process- and product-specific variations as well as variations that are caused by changes in a subgroup mean and those that are caused by changes in the standard deviation.
• Track multiple characteristics on the same chart.

### Group Target Xbar-R Chart

The group target Xbar-R chart provides information about changes in process averages and the range of averages across multiple measurement subgroups of similar characteristics that have a common process. Part numbers and engineering nominal values can differ across these characteristics.

• Track multiple characteristics or similar characteristics with different averages on the same chart.
• View both product and process characteristic variations.
• See the difference between variations that are caused by changes in average and those caused by changes in the standard deviation.

### Group Short Run Xbar-R Chart

When you need to evaluate changes in the process average and range of averages across multiple characteristics in a short run environment, use the group short run Xbar-R chart.

• See the variations of multiple process or product characteristics on one chart, even within short production runs.
• Analyze characteristics from multiple parts with different means, standard deviations, and units of measure.
• Easily separate process- and product-specific variations as well as variations that are caused by changes in a subgroup mean and those that are caused by changes in the standard deviation, even in short run environments.

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