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I-MR-R/S How-To¶
This walkthrough builds a complete I-MR-R/S chart from twenty batches of four measurements. The three panels are drawn from two different standard deviations, and this data is chosen to make that visible: the same twenty batches drawn as an Xbar-R chart put every single point outside the limits.
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 batches from an anodizing line. Four parts were measured from each batch and the coating thickness of each was recorded in microns, so each row is one batch and holds one subgroup of four observations.
| Part 1 | Part 2 | Part 3 | Part 4 |
|---|---|---|---|
| 25.26 | 24.80 | 24.60 | 25.01 |
| 25.45 | 25.48 | 25.36 | 25.26 |
| 24.60 | 24.57 | 24.83 | 24.77 |
| 24.52 | 24.37 | 24.60 | 24.68 |
| 25.03 | 25.52 | 25.07 | 25.70 |
| 24.68 | 25.08 | 24.36 | 24.72 |
| 24.38 | 24.32 | 24.62 | 24.42 |
| 25.40 | 24.93 | 25.56 | 25.23 |
| 24.03 | 24.34 | 24.36 | 24.02 |
| 25.19 | 25.35 | 25.11 | 25.34 |
| 24.44 | 24.72 | 24.74 | 24.58 |
| 25.47 | 25.58 | 25.66 | 25.53 |
| 25.47 | 25.43 | 25.07 | 25.63 |
| 25.21 | 24.72 | 25.01 | 24.99 |
| 24.26 | 24.32 | 23.82 | 24.17 |
| 27.91 | 28.36 | 28.48 | 28.54 |
| 24.10 | 24.36 | 24.57 | 24.07 |
| 24.44 | 24.89 | 24.55 | 24.78 |
| 25.69 | 25.54 | 25.52 | 25.69 |
| 25.10 | 25.25 | 25.54 | 25.38 |
Two things are worth noticing before you chart it. The four parts within any one batch agree closely: no row spans more than 0.72 microns. The batches themselves do not agree nearly as well: batch means run from 24.14 to 25.61 even before batch 16, whose four readings all sit around 28.
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. Headers land in row 1 and the twenty batches 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 > I-MR-R/S.
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Give it the cells
In the Data Selection window set Selected Range: to A1:D21. Leave Data in Columns selected and First Row/Column is Header checked. Press Next >.
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Select all four part columns
The I-MR-R/S Chart dialog opens on the Data tab. Check Part 1 through Part 4 in the measurement list.
There is no Chart: variant row on this dialog
Every other subgrouped chart lets you pick which panels to draw. This one always draws all three. The only panel that changes is the bottom one, and it changes from the Estimate Sigma group rather than from a panel selector.
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Tell it the subgroups run across the columns
In the Subgroups group, select Subgroups across columns.
This decides what your four checked columns mean. Under the default Constant size: mode, four checked columns would give you four separate charts of one measurement each. Under Subgroups across columns, each row becomes one subgroup of four observations and you get a single chart with twenty points on each panel.
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Finish
Press Finish. The chart is written to a new worksheet named I-MR-RS Chart and the Control Chart analysis pane opens on the right. The tab has no slash in it because Excel does not allow one in a sheet name; the title cell on the sheet itself still reads I-MR-R/S Chart.
What you should see¶
Three stacked panels on one worksheet, twenty points on each. The top panel plots the twenty batch means, the middle panel the moving ranges of those means, and the bottom panel the range inside each batch. The first position on the Moving Range panel is blank, because a moving range needs a previous batch to measure against.
| Center line | Lower control limit | Upper control limit | |
|---|---|---|---|
| Individuals Chart | 25.08 | 22.45 | 27.72 |
| Moving Range Chart | 0.99 | 0 | 3.24 |
| Range Chart | 0.43 | 0 | 0.98 |
Batch 16 signals on the Individuals panel. Its mean plots at 28.32, above the upper control limit of 27.72, 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 16 and 17 are both out of control, at 4.18 and 4.05 against an upper limit of 3.24. One moving range measures the step up into batch 16 and the next measures the step back down out of it, so a single wild batch always disturbs two of them. This is the same behaviour as the Moving Range panel of an I-MR chart, applied to batch means instead of single measurements.
The Range panel is quiet. The largest range in the data is 0.72, against an upper limit of 0.98, so nothing is marked. Batch 16 is not unusual here at all: its four parts agree with each other as closely as any other batch's. The batch moved as a whole.
Where each panel's limits came from. The three panels are not drawn from one estimate, and the summary table reports both:
| Estimate | Value | Built from | Draws |
|---|---|---|---|
| Standard deviation of the subgroup means | 0.88 | the average moving range of the means, 0.99, divided by 1.128 | Individuals and Moving Range panels |
| Within-subgroup standard deviation | 0.21 | the average range, 0.43, divided by 2.059 | Range panel |
| Between-subgroup standard deviation | 0.87 | the two above, combined | nothing; it is reported, not drawn |
The Individuals limits sit three times 0.88 either side of the center line, which is why the band is 2.64 microns wide on each side. Nothing about the subgroup size enters that, so those lines would be equally flat on data whose subgroups differed in size. The Range panel's center line of 0.43 is the average of the twenty ranges, and its limits are fixed multiples of it. The formulas are on the Math Details page.
What an Xbar-R chart does with the same twenty batches. An Xbar panel builds its limits from the within-subgroup spread divided by the square root of the subgroup size: 0.21 over 2, which is 0.10. Three of those gives a band 0.31 wide on each side instead of 2.64, more than eight times narrower, with limits at 24.77 and 25.39. Run this same data as Xbar-R and sixteen of the twenty points are marked, thirteen of them outside the control limits and the rest by the pattern tests. Only points 1, 2, 5 and 14 come through unmarked. The Range panel comes out identical to the one above, because both charts estimate the within-subgroup spread the same way.
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 all three panels, each against its own center line and limits; rules 5 through 8 on the Individuals panel only. See Out-of-Control tests.
Things to try next¶
- Run the same data as Xbar-R. Start again from Charts in Subgroups > Xbar-R with the same range and the same Subgroups across columns setting. You get the twenty means plotted against limits of 24.77 and 25.39, with sixteen of them marked. The plotted points are identical on both charts; only the limits differ.
- Stop batch 16 inflating its own limits. Modify the analysis and set Estimate Limits From to the first 15 subgroups. The batch is then outside the estimate that sets the limits: the Individuals limits tighten to 23.19 and 26.60, the Moving Range upper limit drops from 3.24 to 2.10, and batch 16 lands 1.72 above the limit rather than 0.61. It is still the only marked mean.
- Switch the bottom panel to an S Chart. On the Limits and Estimation tab choose Sbar (average standard deviation). The bottom panel becomes an S Chart, plotting each batch's standard deviation instead of its range, and the Use unbiased constants (within sigma) checkbox becomes live. The top two panels do not move, because the standard deviation of the subgroup means is never one of the three Estimate Sigma choices.
- Split the chart. Add a split at batch 16 and each phase gets its own grand mean, its own estimates, and its own limits on all three panels. The Moving Range chain restarts too, so the first position of the second phase is blank as well. See the Split Control Limits section of the Options page.