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Xbar-mR-s Chart Help

There are times when the “within subgroup” variation is significantly different from the “between subgroup” variation. When this occurs, the control limits the Xbar chart in a Xbar-R or Xbar-s combination are very tight and many of the points are out of control. For example, you might have a batch process where you sample a batch four times and use those four samples to form a subgroup. The range between those four subgroups is very small. Using that average range to calculate the control limits for the Xbar chart is what causes the control limits to be so tight. The solution for this type of problem is to use three charts: Xbar-mR-R or the Xbar-mR-s.

This page shows how to create the Xbar-mR-s chart. With the Xbar-mR-s chart, the subgroup averages are plotted on the Xbar chart. The mR is used to monitor the variation in the range between consecutive subgroup averages. The s chart is used to monitor the variation in the within subgroup standard deviation. The data can be downloaded at this link. This page contains the following:

Data Entry

Suppose we are producing a chemical from a batch reactor. We take four samples from each batch and use those four samples to form subgroups. You enter the data are entered into a worksheet as shown below The data does not have to start in A1. It can be anywhere on the spreadsheet. The data can be in rows or in columns.

Creating a New Xbar-mR-s Chart

This is all that is needed to make the control chart. If you select OK at this point, the software will generate the control chart using the default options. Simple and quick.

The options on the input screen are:

Options for the Xbar-mR-s chart

On the input screen for the Xbar-mR-s chart, there is a button labeled “Show Options”. If you select that button, the input screen will show the options available for the chart. It is not required to select any of these options.

Each option is described below.

Out of Control Tests

If you select the Out of Control Tests, the input screen, Tests for Out of Control Points, is displayed below.

These options include:

Note: only four of these tests apply to the s and mR chart:

Control Limit Options

If you select the “Control Limit Options” button, the following is displayed.

The options include:


Titles and Formats

If you select the “Title and Formats” button, the following screen is displayed:

The options include:

Manual Control Limits

If you select the “Manual Control Limits” button, the following screen is displayed:

The options include:

Chart Location

If you select the “Chart Location” button, the following screen is displayed.

The options are:


Box-Cox Transformation

Selecting the “Box-Cox Transformation” button displays the following screen:

The options are:


Process Capability

The “Process Capability” button gives you the option to “tie” a control chart to a process capability chart. This is different from running a process capability option by itself. When the process capability is tied to a control chart, the estimated sigma is based on the option you selected to estimate the value of sigma for the range chart for that control chart. For example, you might have 20 subgroups and split the control limits for the last 10 subgroups. In that case, the process capability (when it is tied to a control chart) will be based on the estimated sigma for the last ten subgroups. When you run a process capability by itself, it would use all the 20 subgroups to estimate sigma. If you manually enter the value of sigma to use for the control chart (see Manual Control Limits above), the software will use that value of sigma for the process capability analysis. The process capability chart is added to a new chart sheet.

If you select the “Process Capability” option, the following input screen is shown. You must enter a name for the control chart before this input screen will show. In the example below, the name of the control chart is Reactor. The name of the process capability chart will be the name of the control chart plus “Cpk” – or ReactorCpk in this example.

The options include:

Updating the Xbar-mR-s Chart with New Data

This control chart can be easily updated with new data after it has been added to the spreadsheet. Please see Updating Control Charts with New Data to see how the software finds the new data and updates the control chart.

Changing the Options for the Xbar-mR-s Chart

You can change the current options for this control chart (e.g., adding a Box-Cox transformation) by selecting “Options” on the Updating/Options panel on the SPC for Excel Ribbon.

The list of available charts in the workbook will be displayed. Select the chart you want to change options for. The input screen for that chart will be shown and changes can be made. See Changing Chart Options for more information

In addition, once a control chart is made, there are numerous actions you can take on the chart including splitting control limits, removing points from the calculations, adding comments, selecting the range on which to base control limits, etc. Please see Control Chart Actions for details.

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