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EWMA¶
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QXL Stat Tools Tab > Control Charts > Time Weighted Charts > EWMA
An EWMA chart (exponentially weighted moving average) is a single panel that plots a smoothed statistic instead of the measurements themselves. Each plotted point is a weighted blend of the current value and the point before it, so every point carries some of the influence of every point that came before, and the influence of an older value fades as the chart moves on. The EWMA weight (λ) decides how fast it fades.
The dialog is titled EWMA Chart, the single panel it draws is the EWMA Chart panel, and the worksheet it writes is named EWMA. Every option in that dialog is described on the Options page.
When to use it¶
- Your measurements are continuous, and you collect them one at a time or in subgroups. Both work here. Unlike the subgroup charts, a constant subgroup size of 1 is accepted, and that makes it a chart of individual values.
- You want each point to reflect recent history rather than only the latest subgroup. A shift that is too small to push a single Shewhart point past a limit accumulates in the smoothed statistic instead, which is the reason this chart exists.
- You do not need a capability analysis attached to the chart. EWMA has no Capability tab, and no capability index or histogram is produced, whatever specification limits are stored elsewhere in the analysis.
If you want a chart of the measurements themselves, with a companion panel for the spread, use Xbar-R, Xbar-S, or I-MR. If you want the deviations from a target accumulated instead of smoothed, use CUSUM, the other chart in the Time Weighted Charts group.
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. With a constant subgroup size of 1 there is nothing to average, and the value in the row is used as it stands.
Those values are then smoothed. The first smoothed value starts from the center line, and each one after it is the weighted average of its own value and the smoothed value before it, using the weight λ you set. A large λ leaves the chart close to the raw values; a small λ makes it slower to move and gives it a longer memory.
The center line is the grand mean of the individual observations, and it does not move. The limits do. Because the smoothing starts from a fixed value, the smoothed statistic has almost no accumulated variation at the first point and more at each point after it, so the control limits start narrow at the center line and widen, quickly at first and then hardly at all, toward a steady width. That funnel shape at the left of the chart is the visual signature of an EWMA chart and is not a drawing artifact. The width at each point is built from the within-subgroup standard deviation, the weight, the point's position in the series, and each subgroup's own size, so unequal subgroup sizes are handled point by point.
Which estimates of the within-subgroup standard deviation are offered depends on the shape of your data, and the dialog swaps them as you change the subgroup size. With subgroups of two or more it offers Rbar, Sbar, and the pooled standard deviation. With a constant subgroup size of 1 it offers the average moving range, the median moving range, and the square root of MSSD instead.
Three settings change what the limits describe rather than how they are computed. Estimate Limits From computes them from the first few subgroups only. Split Control Limits divides the chart into phases, each with its own center line, its own limits, and its own restarted smoothing. A Transformation rescales the measurements before any of this happens. Manual limits are the one thing this chart does not offer: a widening band has no single set of values to type in.
The exact formulas are on the Math Details page.
Output¶
The analysis writes one worksheet per chart, named EWMA. Under GroupBy each worksheet name gains " - " and the group name. On the sheet, 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 EWMA Chart panel, plotting the smoothed statistic with its center line and its widening control limits, plus the zone lines, reference lines, and phase dividers if you asked for them. Points that broke the out-of-control test are drawn in a different color.
- A summary table to the right, listing the center line, the control limits, 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.
One row of that table needs reading with care. The limits move from point to point, so the single UCL and LCL reported are the limits at the last plotted point, which is the widest pair on the chart. They are not the limits the early points were judged against.
There is never a capability block or a histogram on an EWMA sheet. The engine switches both off for this chart rather than leaving them for the dialog to hide.
When the analysis finishes, the Control Chart task pane opens on the right. See Options for what it can and cannot change.