Home / Statistical Tools / Control Charts / Xbar-S
Xbar-S¶
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QXL Stat Tools Tab > Control Charts > Variables > Charts in Subgroups > Xbar-S
An Xbar-S chart is two stacked panels built from measurements collected in subgroups. The upper panel, Xbar Chart, plots the mean of each subgroup. The lower panel, S Chart, plots the standard deviation of each subgroup. Read the S panel first: the limits on the means are computed from the within-subgroup spread, so the spread has to be stable before the means are worth judging.
The dialog is titled Xbar-S Chart and the worksheet it creates is also named Xbar-S Chart. Every option in that 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.
- The subgroups are large enough that you want every observation in each one to contribute to the spread estimate. A standard deviation uses all of the values in a subgroup, where a range uses only the largest and the smallest.
- You want the limits on the means to reflect only the variation inside a subgroup, so that a shift between subgroups shows up as a point outside the limits rather than being absorbed into wider limits.
If your subgroups are small and you would rather read a range, use an Xbar-R chart. If your process gives you one measurement at a time, use an I-MR chart instead. If you want only the lower panel, the ribbon has a separate S entry, which opens this same dialog with the S only variant selected.
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. Each subgroup contributes its mean and its standard deviation, and those are what the two panels plot.
The center line of the Xbar panel is the grand mean of the individual observations. With unequal subgroup sizes that is not the same as the average of the subgroup means, because a larger subgroup carries more weight.
The limits come from a single within-subgroup standard deviation estimated once for the whole chart, using either Sbar (the default, built from the subgroup standard deviations) or the pooled standard deviation. Rbar is not offered here, because the companion panel on this chart plots standard deviations rather than ranges. The Xbar limits sit a number of standard errors either side of the center line, and the standard error uses each subgroup's own size: equal sizes give straight lines, unequal sizes give limits that step in where a subgroup is large and out where it is small.
The S panel uses the same estimate. Its center line is the standard deviation expected from a subgroup of that size, so it steps with subgroup size too, and its limits are fixed multiples of it. The lower limit is held at zero. A subgroup with fewer than two values has no standard deviation, so that position is empty on the S panel while its mean is still plotted above.
One setting on this chart changes the shape of the S panel rather than just its width. Use unbiased constants (within sigma) is live on Xbar-S, because both estimators offered here apply an unbiasing constant, unlike Rbar on an Xbar-R chart where the correction is always part of the estimate and the checkbox is greyed out. Clearing it flattens the S panel's center line to a single value at every point while the limits keep stepping, so the band becomes visibly asymmetric about a straight center line.
Two further 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 line and limits.
The exact formulas are on the Math Details page.
Output¶
The analysis writes one worksheet per chart, named Xbar-S 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. 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 S Chart panel below it, aligned so its points line up vertically with the panel above.
- 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 Create Control Charts for what it can and cannot change.