## About this lesson

The X-bar and Standard Deviation chart is the variable data control chart used when the subgroup is large. This lesson explains how the data is recorded and interpreted on the pair of control charts. The lesson describes how to create this control chart in both Microsoft Excel and using Minitab. The lesson will include practice creating the charts.

## Exercise files

Download this lesson’s related exercise files.

Xbar-S Chart.xlsx12.6 KB Xbar-S Chart - Solution.docx

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## Quick reference

### Xbar-S Chart

The Xbar-S chart (Subgroup Mean and Standard Deviation) are the variable data control chart to be used when working with a subgroup sample that has ten or more units. It can be easily created in either Microsoft Excel or Minitab.

### When to use

Use the Xbar-S Chart when seeking to control a product or process variable parameter with a high volume process. With high volume and a large number of data points, the standard deviation is a better gauge of the subgroup variation than is the range from max value to min value. The standard deviation uses all the data points and is not as easily impacted by an outlier.

### Instructions

The Xbar-S is comprised of a pair of control charts. These are normally aligned so that the Subgroup Mean (Xbar) chart is directly above the Standard Deviation 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 Standard Deviation chart plots the value of the standard deviation for all the subgroups. The standard deviation is always a positive number.

One other advantage of the Xbar-S chart is that it can work with subgroup sizes that vary slightly. However, they should always be greater than 10 data points. When the subgroup sizes are not equal, the control limit lines will not be straight lines but rather will be stair-stepped. This is because the constants used in the equations change with changing subgroup sample size.

Xbar-S 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-S.” In the Minitab Xbar-S 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 all the data is in one column, the data subgroups must have the same number of points. If they don’t you must use the different column approach.

If creating the Xbar-S 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 standard deviation for each subgroup. These will be the values that are plotted.
- Calculate the global mean for all the data points and the mean for the standard deviation values.
- Calculate the upper and lower control limits for the standard deviation plot.
- If the Standard Deviation 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 Standard Deviation in its control limit calculations.
- Now calculate the control limits for the Subgroup Mean data points.
- Plot the Subgroup mean, Standard Deviation, 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 A3, B3 and B4 constant values.
- Don’t select arbitrary subgroups, they should relate to the physical process or calendar groupings.
- The popularity of the Xbar-S chart is growing. When SPC was done manually, collecting the additional data points for an Xbar-S chart often required much more time. But the improved process knowledge was minimal as compared to an Xbar-R chart. In today’s business world with automation and the Internet of Things, there is plenty of data and processing it is essentially free. So this chart is being used more often.

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