Xbar-Range (Xbar-R) Chart

Chart Components

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

Xbar-R Charts for a Single Characteristic

Traditionally, an Xbar-R chart is used to plot a subgroup mean for smaller subgroups and the range of individual values for a single characteristic. 

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

Xbar and r Charts for a Single Characteristic

How 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 uses discussed for this chart all deal with sample sizes between 2 and 9.

Advantages and Disadvantages of Using the Xbar-R Chart

Advantages
  • 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
Disadvantages
  • 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.
xbar and r chart example

Special Uses

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

x bar chart
 

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.
 
See an Example Use Case

xbar and r chart formula

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.
 
See an Example Use Case

xbar and r interpretation of charts

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.
 
See an Example Use Case

the difference between xbar and r 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.
 
See an Example Use Case
The construction of xbar and r chart

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.

See an Example Use Case

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