Home / Statistical Tools / Control Charts / Xbar-R and Xbar-S / Xbar-R How-To
Xbar-R How-To¶
This walkthrough builds a complete Xbar-R chart from twenty subgroups of five measurements, using the Subgroups across columns layout. One subgroup in the data is out of control, so the finished chart has something to find.
The data is on this page rather than in a file to download. Press Copy for Excel, then paste it into a blank worksheet.
The data¶
Twenty hours of production. Five fasteners were checked each hour and the seating torque of each was recorded in inch-pounds, so each row is one hour and holds one subgroup of five observations.
| Reading 1 | Reading 2 | Reading 3 | Reading 4 | Reading 5 |
|---|---|---|---|---|
| 51.3 | 51.4 | 50.1 | 49.2 | 48.9 |
| 50.0 | 49.0 | 48.6 | 50.2 | 50.1 |
| 50.5 | 49.1 | 50.0 | 49.9 | 48.5 |
| 50.5 | 50.3 | 52.4 | 50.2 | 49.9 |
| 51.2 | 50.2 | 50.9 | 49.6 | 50.2 |
| 51.0 | 50.7 | 50.1 | 48.9 | 50.4 |
| 50.1 | 50.7 | 50.2 | 51.1 | 49.9 |
| 50.2 | 50.7 | 48.9 | 49.6 | 49.5 |
| 52.0 | 49.9 | 50.7 | 50.6 | 49.7 |
| 48.4 | 51.0 | 49.6 | 50.7 | 48.7 |
| 49.6 | 51.3 | 51.4 | 48.7 | 48.7 |
| 50.0 | 50.7 | 50.2 | 50.3 | 49.0 |
| 50.6 | 51.1 | 49.6 | 48.6 | 49.2 |
| 50.8 | 48.3 | 49.9 | 49.0 | 49.9 |
| 52.3 | 52.5 | 54.0 | 52.9 | 53.8 |
| 49.9 | 49.5 | 50.4 | 47.2 | 50.0 |
| 50.2 | 48.8 | 50.5 | 49.4 | 47.5 |
| 49.8 | 49.0 | 49.5 | 49.8 | 51.3 |
| 50.1 | 50.0 | 50.4 | 48.2 | 51.2 |
| 48.9 | 50.4 | 48.9 | 49.0 | 49.6 |
The fifteenth row is the one to watch. All five of its readings sit two to four inch-pounds above the rest of the data, and they are close together, so that hour's mean moved but its spread did not.
Steps¶
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Put the data in Excel
Press Copy for Excel above the table. In Excel, open a blank worksheet, click cell A1, and press Ctrl+V. You should have headers in row 1 and data in rows 2 through 21.
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Start the chart
From the Excel ribbon: QXL Stat Tools Tab > Control Charts > Variables > Charts in Subgroups > Xbar-R.
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Give it the cells
The Data Selection window opens first. Set Selected Range: to A1:E21, either by typing it or by selecting it on the sheet.
Leave Data in Columns selected and leave First Row/Column is Header checked. Both are already correct here: the range has more rows than columns, and the first cell holds text. Press Next >.
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Select all five reading columns
The Xbar-R Chart dialog opens on the Data tab. Check all five columns, Reading 1 through Reading 5, in the measurement list.
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Tell it the subgroups run across the columns
In the Subgroups group, select Subgroups across columns.
This is the step that decides what your five checked columns mean. Under the default Constant size: mode, five checked columns would give you five separate charts of one measurement each. Under Subgroups across columns, each row becomes one subgroup of five observations and you get a single chart with twenty points.
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Finish
Press Finish. The chart is written to a new worksheet named Xbar-R Chart and the Control Chart analysis pane opens on the right.
What you should see¶
Two stacked panels on one worksheet, with twenty points on each.
| Center line | Lower control limit | Upper control limit | |
|---|---|---|---|
| Xbar Chart | 50.07 | 48.80 | 51.35 |
| Range Chart | 2.22 | 0 | 4.68 |
One point out of control. Point 15 on the Xbar Chart plots at 53.10, well above the upper control limit of 51.35, and is drawn in a different color from the rest of the series. It is the only marked point on either panel.
The Range Chart is quiet. Every range falls inside its limits. Together the two panels say the spread inside an hour did not change and the hour-to-hour level did, which is what you would expect from data where one subgroup was shifted as a whole.
Where the limits came from. The Xbar Chart limits are not three standard deviations of the twenty plotted means. They are built from the variation inside the subgroups: the average range of 2.22 gives a within-subgroup standard deviation of 0.95, that is divided by the square root of the subgroup size to get the standard error of a mean, and the limits sit three of those either side of the center line. That is why a subgroup whose five readings agree closely with each other, but disagree with the rest of the chart, lands so far outside. The formulas are on the Math Details page.
Which test flagged the point
All eight out-of-control tests are on by default on this chart, and Quantum XL does not report which one marked a given point. Every enabled test is combined into a single result per point, and the point is simply drawn in a different color. See Out-of-Control tests.
Things to try next¶
- Remove the signal. Modify the analysis and set Estimate Limits From to the first 14 subgroups. The limits are then computed without the shifted hour and extended across the whole chart, and point 15 sits even further outside them.
- Split the chart. Add a split at point 15 and each phase gets its own center line and limits. See the Split Control Limits section of the Options page.
- Use one panel. Change the Chart: radio group at the top of the dialog to Xbar only or R only to draw a single panel from the same data.