## About this lesson

The X-bar and Range chart is the most commonly used variable data control chart. When discussing SPC, this is always the example. This lesson explains how the data is recorded and interpreted on the chart. The lesson describes how to create this control chart in both Microsoft Excel and using Minitab. The lesson will include practice creating the chart.

## Exercise files

Download this lesson’s related exercise files.

Xbar-R Chart.xlsx11.5 KB Xbar-R Chart - Solution.docx

207.9 KB

## Quick reference

### Xbar-R Chart

The Xbar-R chart (Subgroup Mean and Range) are the variable data control chart to be used when working with a subgroup sample of two to ten units. It can be easily created in either Microsoft Excel or Minitab.

### When to use

Use the Xbar-R Chart when seeking to control a product or process variable parameter. It is the most commonly used variable data control chart. It can be used with both high volume and low volume processes. It is more sensitive to shifts in the mean than the I-MR chart. And it is quite easy to do the math associated with calculating the control limits.

### Instructions

The Xbar-R is comprised of a pair of control charts. These are normally aligned so that the Subgroup Mean (Xbar) chart is directly above the Range chart. This aids in the recognition of special cause occurrences. The Subgroup Mean chart plots the average value of the data points that were used to sample the subgroup. The Range chart plots the value of the difference between the largest point and the smallest point in the subgroup data points. Therefore the Range value is always a positive number – even if all the data values were negative numbers.

Xbar-R Charts can be created in Microsoft Excel or in Minitab. Within Minitab, control charts are created by using the “Stat” pull down menu, then selecting “Control Charts.” Within the Control Charts window, select “Variable Charts for Subgroups” and then finally select “Xbar-R.” In the Minitab Xbar-R Chart panel, you will need to select the data columns with your data. If all the data is in one column, you will need to tell Minitab how many data points are in each subgroup.

If creating the Xbar-R Chart in Excel:

- Measure the attribute for the first item in the subgroup sample and record the data in a column in Excel. Then measure the next item in the subgroup sample and record that in the next column. By doing this, each row in Excel represents a subgroup.
- In an adjacent column, calculate the Mean for each subgroup and then calculate the range from the smallest to the largest data point in the subgroup. These will be the values that are plotted.
- Calculate the global mean for all the data points and the mean for the Range values.
- Calculate the upper and lower control limits for the Range plot. The lower control limit is zero for this chart if the number of data points in the subgroup is seven or less.
- If the Range plot shows an out of control condition, it must be corrected before proceeding to the Subgroup Mean plot, since that plot relies on the mean of the Range in its control limit calculations.
- Now calculate the control limits for the Subgroup Mean data points.
- Plot the Subgroup mean, Range, the calculated Means and the control limits.
- Take appropriate actions to remove special causes or to center your data within the customer spec limits.

### Hints & tips

- Remember you are plotting the mean of the data, not the actual data.
- Be sure to use the subgroup sample size when selecting the A2, d3 and d4 constant values.
- Don’t select arbitrary subgroups, they should relate to the physical process or calendar groupings.

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