Home / Statistical Tools / Control Charts / I-MR-R/S
I-MR-R/S¶
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QXL Stat Tools Tab > Control Charts > Variables > Charts in Subgroups > I-MR-R/S
An I-MR-R/S chart is three stacked panels built from measurements collected in subgroups. It always draws all three. There is no variant of this chart that hides a panel, and no ribbon entry that opens it with fewer.
| Panel | Title on the worksheet | What it plots | Y axis |
|---|---|---|---|
| Top | Individuals Chart | the mean of each subgroup | Subgroup Mean |
| Middle | Moving Range Chart | the moving range of those subgroup means | Moving Range of Means |
| Bottom | Range Chart or S Chart | the spread inside each subgroup | Range, or Standard Deviation |
The first panel is titled Individuals Chart, but the "individual" it charts is a subgroup mean, not a single measurement. Each subgroup contributes one point to it, and the band around those points is built from how much consecutive subgroup means differ, not from the spread inside a subgroup divided by the square root of the subgroup size. That is the whole difference between this chart and an Xbar-R or Xbar-S chart drawn from the same data.
The bottom panel is not fixed. It is a Range Chart when the sigma estimation method is Rbar or the pooled standard deviation, and an S Chart when the method is Sbar. No other chart in Quantum XL changes what a panel is in response to an estimation setting.
The dialog is titled I-MR-R/S Chart. The worksheet it creates is named I-MR-RS Chart, without the slash, because a slash is not allowed in an Excel sheet name. The title cell of the User Input block on that same worksheet still reads I-MR-R/S Chart, so the tab name and the title written on the sheet do not match. Every option in the dialog is described on the Options page.
When to use it¶
- Your measurements are continuous, and you collect two or more of them per point in time: five parts an hour, three samples per batch, four cavities per shot.
- You want the variation between subgroups charted separately from the variation inside a subgroup. The top two panels are built from the subgroup means alone; the bottom panel is built from the within-subgroup spread alone.
- You want the band on the subgroup means to come from how much consecutive means differ, so that a source of variation acting between subgroups widens the limits instead of throwing points outside them.
- The subgroup sizes are mostly the same. The sigma behind the top two panels is estimated from subgroups of the most common size only, so a data set with no dominant subgroup size leaves those two panels without limits.
If you want the limits on the means built from the within-subgroup spread instead, use an Xbar-R or Xbar-S chart. If your process gives you one measurement at a time, use an I-MR chart.
How it works¶
Quantum XL divides your rows into subgroups: a constant number of consecutive rows, an identifier column whose repeated value marks a subgroup, or one subgroup per row built across several measurement columns. The smallest constant subgroup size the dialog accepts is 2, because a subgroup of one has neither a range nor a standard deviation for the bottom panel.
Two different standard deviations are estimated, and each one owns part of the chart.
The standard deviation of the subgroup means is estimated from the moving ranges of the subgroup means. It sets the lines on the top two panels. Only subgroups whose size equals the most common size contribute to it: a subgroup of any other size breaks the chain of consecutive means, the same way a missing value breaks a chain. The most common size must also account for more than half of the subgroups. When it does not, this estimate does not exist, and the top two panels are drawn with their points but without a center line or limits.
The within-subgroup standard deviation is estimated by Rbar (the default), Sbar, or the pooled standard deviation. It sets the lines on the bottom panel. This is the only chart in the product that offers all three of those methods in one dialog, and the choice does more than change a number: it also decides whether the bottom panel is a Range Chart or an S Chart.
From those two estimates the three panels are drawn:
- The Individuals Chart centers on the grand mean of the individual observations and puts its limits a number of standard deviations of the subgroup mean either side of it. No subgroup size enters those limits, so they are straight lines even when the subgroups differ in size.
- The Moving Range Chart plots the moving range of the subgroup means and centers on a constant multiple of the same standard deviation of the subgroup means. On this chart the moving range length is fixed at 2, so every plotted value is the difference between one subgroup mean and the one before it, and the first position on the panel is empty because it has no predecessor.
- The Range Chart or S Chart behaves exactly as the companion panel of an Xbar-R or Xbar-S chart does. Its center line is the range or the standard deviation expected from a subgroup of that size, so it steps when the subgroup sizes differ, and its limits are fixed multiples of it. The lower limit is held at zero.
This chart is also the only one that lets you supply a between-subgroup mean and standard deviation as historical values, alongside the mean, overall, and within boxes the other subgrouped charts offer.
Two settings change what the limits describe rather than how they are computed. Estimate Limits From computes them from the first few subgroups only and extends them across the whole chart. Split Control Limits divides the chart into phases, each with its own center lines and limits.
The exact formulas are on the Math Details page.
Output¶
The analysis writes one worksheet per chart, named I-MR-RS Chart. On it, from the top:
- A User Input block in the first two columns, holding the analysis title, the columns you selected, and whether the calculation type was Excel or GroupBy. Its title cell reads I-MR-R/S Chart, with the slash, unlike the worksheet tab. Modify Existing Analysis reads this block back.
- The Individuals Chart panel, plotting each subgroup mean with its center line and control limits, plus the zone lines, reference lines, and phase dividers if you asked for them. Points that broke an enabled out-of-control test are drawn in a different color.
- The Moving Range Chart panel below it, plotting the moving range of those means.
- The Range Chart or S Chart panel at the bottom, whichever the sigma estimation method selected. All three panels are aligned so their points line up vertically.
- A summary table to the right, listing for each panel the center line, the control limits where they exist, the count of out-of-control points, and the count of points you marked as outliers. A transformation adds rows naming the type and its parameters; a split chart adds a per-phase breakdown.
- A capability and histogram block below the panels, but only when you entered a specification limit or a target on the Capability tab.
When the analysis finishes, the Control Chart task pane opens on the right. See Options for what it can and cannot change.