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u Chart¶
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QXL Stat Tools Tab > Control Charts > Attribute Charts > C, U, and Laney's U'
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How-To works through a finished chart step by step, from sample data you copy off the page straight into Excel. The data has a point that is out of control, so the result has something to read rather than twenty points in a row.
How-To with GroupBy does the same thing with a GroupBy column, so one run produces a separate chart per group.
A u chart monitors defects per unit when the area of opportunity varies. It counts defects rather than defective items, so one item can contribute several, and it divides by the size of each subgroup so subgroups of different sizes sit on one chart.
| Panel title on the worksheet | U Chart, one panel only |
| What it plots | defects divided by inspection size, for each subgroup |
| Y axis | Defect Rate |
| X axis | Subgroup |
| Distribution behind the lines | Poisson |
One ribbon entry opens three charts. The button reads C, U, and Laney's U', and a Variant: radio row at the top of the dialog chooses between C, U and Laney U'. The dialog opens on U, not on C, whichever order the button names them in. The window title and the worksheet name follow the variant.
When to use it¶
- You count defects, and the area of opportunity varies between subgroups: different numbers of units, different areas, different time windows.
- If the area of opportunity is constant, the c Chart plots the raw counts instead and its limits are straight lines. It is the same dialog with the variant on C.
- If the counts scatter more than the Poisson model predicts, the Laney U' Chart widens the limits to match. Every u chart reports the diagnostic that tells you whether that is happening.
How it works¶
The center line is \(\bar{u}\), the pooled defect rate: total defects divided by total inspection size across the baseline subgroups. It is not the average of the subgroup rates, and the two differ whenever the sizes differ.
Each point is that subgroup's own rate. The center line is flat and the limits step: the standard deviation of a rate is \(\sqrt{\bar{u}/n_i}\), so a larger inspection size gives a tighter band. The lower limit is held at zero, since a rate cannot be negative. There is no upper cap, unlike a p chart's cap at 1: a defect rate has no ceiling, because one unit can carry any number of defects.
Every u chart also reports \(\sigma_Z\), an overdispersion diagnostic comparing the scatter present with the scatter the Poisson model predicts. Near 1 means the model fits. Substantially above 1 means the limits here are tighter than the process deserves. It is computed and printed but not applied: applying it is what makes the chart a Laney U' Chart.
Two settings change what the limits are estimated from rather than how. Baseline Estimation estimates \(\bar{u}\) from the first few subgroups and extends it. Split Control Limits divides the chart into phases and re-estimates inside each one. A Historical uBar box supplies a known rate outright, and Force Straight Limits substitutes one assumed inspection size into the limits while leaving the center line alone.
The exact formulas are on the Math Details page.
Output¶
The analysis writes one worksheet named U Chart. Under GroupBy there is one worksheet per group, each named U Chart - {GroupName}.
Worksheets are divided by GroupBy group, not by chart. Every chart belonging to a group is stacked down that one worksheet, one below the other, so selecting three measurement columns without GroupBy produces three charts on a single sheet rather than three sheets. The User input block is written once at the top of each worksheet; everything after it repeats for each chart on the sheet.
On the sheet, from the top:
- A User Input block in the first two columns, holding the analysis title, the defects column, the inspection size column or constant, the X-axis label column and any GroupBy columns, then a Settings block stating the options that produced the sheet. Modify reads it back. The rows are listed under What the sheet records about your settings.
- The U Chart panel, plotting each subgroup rate with its stepped limits, any reference lines, and phase dividers when the chart is split. Points that broke an enabled out-of-control test are drawn in a different color.
- A summary table to the right, listing u-bar, UCL, LCL, Total subgroups, OOC points and Outliers marked. The UCL and LCL rows, and the center-line row with them, are read at the LAST plotted point, so on a chart with varying sample sizes read the stepped limits off the chart rather than off the table. A split chart adds a Per-Split Breakdown block.
- An Overdispersion Interpretation block, headed by the computed \(\sigma_Z\) and then a three-row legend for reading it. It is a legend, not a verdict: all three rows are printed and you decide which one applies. On a split chart the pooled \(\sigma_Z\) is not printed at all; each phase reports its own \(\sigma_Z\) in the Per-Split Breakdown instead.
- An optional Z-score plot, off by default, from the Diagnostics group.
There is no capability block and no histogram on an attribute chart worksheet.
When the analysis finishes, the Control Chart task pane opens on the right. See Task Pane for what it can and cannot change.
The Settings block¶
The same block is printed for the U chart, the C chart and the Laney U' chart.
| Row | What it reads |
|---|---|
| Inspection size | Constant followed by the size you typed, which starts at 1000, or By column |
| Control limits | Shewhart, Manual or None |
| k (std devs) | the limit multiple |
| Limits from | All subgroups, or First N subgroups, with the count you set in place of N |
| Split limits | None, By column or Manual break points |
| Break points | the row numbers, comma separated, only with manual break points |
| Historical mean | printed only when you entered one |
| Manual UCL, Manual center, Manual LCL | each printed only when you entered it |
| Straight limits | On or Off |
| Straight limits n | the size, printed only when you entered one |
| Compute sigma Z | On or Off |
| Z-score plot | On or Off |
A C chart prints no Inspection size row. Its inspection size is fixed at one and the dialog's box is disabled, so the row would state a setting your choice cannot affect.
Rules in effect lists only Nelson rules 1 to 4, one row per enabled rule. This chart has no multi-sigma zone rules, so rules 5 to 8 never appear.