Home / Statistical Tools / Control Charts / Xbar-R
Xbar-R¶
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QXL Stat Tools Tab > Control Charts > Variables > Charts in Subgroups > Xbar-R
An Xbar-R chart is a pair of stacked panels built from measurements collected in subgroups. The upper panel, titled Xbar Chart, plots the mean of each subgroup and shows where the process is centered. The lower panel, titled Range Chart, plots the range of each subgroup and shows how much the process varies inside a subgroup. The two are read together, and the range panel is read first: the spread has to be stable before the means are worth judging, because the limits on the means are computed from the within-subgroup spread.
The dialog is titled Xbar-R Chart and the worksheet it creates is also named Xbar-R Chart. Every option in that dialog is described on the Options page.
If you want only one of the two panels, the same dialog offers Xbar only and R only, and the ribbon has separate entries for them.
How it works¶
Quantum XL first divides your rows into subgroups. You choose how: 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. Each subgroup then contributes two numbers, its mean and its range, and those are the values plotted on the two panels.
The center line of the Xbar panel is the grand mean of the individual observations. When the subgroups all hold the same number of values, that is the same thing as the average of the subgroup means; when they do not, it is not, because a larger subgroup contributes more observations and therefore carries more weight.
The width of the limits comes from a single within-subgroup standard deviation estimated once for the whole chart. Two estimators are offered: Rbar, which combines the subgroup ranges and is the default, and the pooled standard deviation, which pools the squared deviations from every subgroup. Whichever you choose, the Xbar limits are placed a number of standard errors above and below the center line, and the standard error uses each subgroup's own size. So subgroups of equal size give the familiar straight pair of lines, and subgroups of unequal size give limits that step in where a subgroup is large and out where it is small.
The Range panel is built from the same within-subgroup estimate. Its center line is the range you would expect from a subgroup of that size, so it steps with the subgroup size as well, and its limits are fixed multiples of that center line. The lower limit is held at zero, since a range cannot be negative, and a subgroup with fewer than two values has no range at all, so that position is left empty on the range panel while its mean is still plotted above.
Two settings change what the limits describe rather than how they are computed. Estimate Limits From lets you compute the limits from the first few subgroups only and then extend them across the whole chart, which is how you freeze a known-good period and judge everything afterwards against it. Split Control Limits divides the chart into phases and gives each phase its own center line and limits, for when you know the process changed on a particular date.
The exact formulas, including the two sigma estimators, the per-point limits, and the range constants they use, are on the Math Details page.
Output¶
The analysis writes one worksheet per chart, named Xbar-R Chart. On it, from the top:
- A User Input block in the first two columns, holding the analysis title (
Xbar-R Chart), the columns you selected, and whether the calculation type was Excel or GroupBy. This is the record of what you asked for, and Modify Existing Analysis reads it back. - The Xbar 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 Range Chart panel below it, aligned so that its points line up vertically with the panel above.
- A summary table to the right of the charts. For each panel it lists the center line, the upper and lower control limits where they exist, the count of out-of-control points, and the count of points you marked as outliers. A transformation adds its own rows naming the type and its parameters, and a split chart adds a per-phase breakdown underneath.
- A capability and histogram block below the panels, but only when you entered a specification limit or a target on the Capability tab. With no specification and no target, no capability output is produced.
When the analysis finishes, the Control Chart task pane opens on the right. It scrolls the display window, shows or hides the zone lines, the out-of-control markers, and the outlier markers, and edits the phase break points. See Options for what it can and cannot change.