Home / Statistical Tools / Control Charts / I-MR / I-MR How-To
I-MR How-To¶
This walkthrough builds a complete I-MR chart from twenty-five single measurements. One of them is out of control, and it shows up on both panels, which is worth seeing once.
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-five consecutive batches of a filling process. One bottle was weighed from each batch, in grams. There are no subgroups: one measurement per batch is all there is, which is exactly the situation I-MR is for.
| Fill Weight |
|---|
| 20.64 |
| 20.72 |
| 20.03 |
| 19.62 |
| 19.45 |
| 20.02 |
| 19.49 |
| 19.28 |
| 20.10 |
| 20.07 |
| 20.27 |
| 19.54 |
| 20.00 |
| 19.97 |
| 19.25 |
| 20.27 |
| 20.16 |
| 23.79 |
| 20.10 |
| 19.93 |
| 20.62 |
| 20.10 |
| 20.45 |
| 19.82 |
| 20.11 |
Batch 18 is the one to watch. Every other reading sits between 19.25 and 20.72; that one is 23.79.
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. The header lands in A1 and the twenty-five readings in A2:A26.
-
Start the chart
From the Excel ribbon: QXL Stat Tools Tab > Control Charts > Variables > Charts as Individuals > I-MR.
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Give it the cells
In the Data Selection window set Selected Range: to A1:A26. Leave Data in Columns selected and First Row/Column is Header checked. Press Next >.
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Check the measurement column
The I-MR Chart dialog opens on the Data tab. Check Fill Weight in the measurement list.
There is no Subgroups group on this dialog
Every chart in the Charts as Individuals family reads one observation per row, so there is no subgroup mode to pick, no identifier column, and no subgroup size box. Each row is one point. This is the main way the dialog differs from Xbar-R's.
It also changes what a second checked column would mean here: it would produce a second chart, not another observation inside a shared point.
-
Finish
Press Finish. The chart is written to a new worksheet named I-MR Chart and the Control Chart analysis pane opens on the right.
What you should see¶
Two stacked panels on one worksheet. The upper panel plots all twenty-five readings. The lower panel plots the moving ranges, and its first position is blank, because a moving range needs a previous point to measure against.
| Center line | Lower control limit | Upper control limit | |
|---|---|---|---|
| Individuals Chart | 20.15 | 18.30 | 22.01 |
| Moving Range Chart | 0.70 | 0 | 2.28 |
The spike signals on the Individuals panel. Point 18 plots at 23.79, above the upper control limit of 22.01, and is drawn in a different color. It is the only marked point on that panel.
It signals twice on the Moving Range panel. Points 18 and 19 are both out of control, at 3.63 and 3.69 against an upper limit of 2.28. That is not a mistake: one moving range measures the jump up into batch 18, and the next measures the jump back down out of it. A single wild value always disturbs two moving ranges, so one upset on the upper panel becomes a pair on the lower one.
Where the limits came from. The average moving range is 0.70. Dividing it by the constant for a window of two, 1.128, gives an estimated standard deviation of 0.62, and the Individuals limits sit three of those either side of the center line. The Moving Range panel's own center line is that same average moving range, and its upper limit is a fixed multiple of it. So the width of both panels traces back to how much consecutive batches differ, not to the overall spread of the twenty-five readings. The formulas are on the Math Details page.
Which test flagged the point
All eight out-of-control tests are on by default, and Quantum XL does not report which one marked a given point. Rules 1 through 4 are tested on both panels; rules 5 through 8 on the Individuals panel only. See Out-of-Control tests.
Things to try next¶
- Stop the spike inflating its own limits. The wild batch is in the estimate that sets the limits, so it widens them. Modify the analysis and set Estimate Limits From to the first 17 points: the limits are then built without batch 18 and it lands further outside.
- Switch to the median moving range. On the Limits and Estimation tab choose Median moving range. The median is barely moved by one large jump, so the limits tighten noticeably. Compare the two sigma values in the summary table.
- Draw one panel on its own. Change the Chart: radio group at the top of the dialog to Individuals or Moving Range. Note that selecting Individuals also switches the sigma method to Square root of MSSD without saying so, which changes the limits.