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c 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.
A c chart monitors the number of defects in each subgroup, where every subgroup covers the same area of opportunity: one panel, one hour of production, one square metre. A single item can carry several defects, so this chart counts defects rather than defective items.
| Panel title on the worksheet | C Chart, one panel only |
| What it plots | the raw defect count in each subgroup |
| Y axis | Count of Defects |
| 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, so this is the one chart in the family you have to select deliberately.
When to use it¶
- You count defects rather than defective items, and the area of opportunity is constant from subgroup to subgroup.
- If the area of opportunity varies, the u Chart divides by it and this chart does not. That is the whole distinction between them, and getting it wrong is the most common mistake on this pair: a c chart of unequal subgroups compares counts that were never comparable.
- If the counts scatter more than the Poisson model predicts, the Laney U' Chart widens the limits. Every c chart reports the diagnostic that tells you whether that is happening.
How it works¶
The center line is \(\bar{c}\), the plain average of the defect counts across the baseline subgroups. This is the one attribute chart where the center line is a simple average, because there are no differing sizes to weight.
The Poisson model sets the spread from the center line: its variance equals its mean, so the standard deviation is \(\sqrt{\bar{c}}\), one number for the whole chart. There is nothing else to estimate and nothing to choose, which is why the dialog offers no sigma method and ignores any historical sigma. Both limits are therefore straight lines, and this is the only attribute chart whose band does not step.
The limits are three standard deviations either side by default, with the lower limit held at zero since a count cannot be negative. There is no upper cap: a subgroup can carry any number of defects.
Every c chart also reports \(\sigma_Z\), an overdispersion diagnostic comparing the scatter present with the scatter Poisson variation predicts. It is computed and printed but not applied: applying it is what makes the chart a Laney U' Chart.
Because a c chart has no inspection size, the whole Inspection Size group in the dialog is disabled when this variant is selected. It greys out rather than being ignored silently.
The exact formulas are on the Math Details page.
Output¶
The analysis writes one worksheet named C Chart. Under GroupBy there is one worksheet per group, each named C 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.
The sheet carries a User Input block, the C Chart panel, a summary table listing c-bar, UCL, LCL, Total subgroups, OOC points and Outliers marked, and an Overdispersion Interpretation block headed by the computed \(\sigma_Z\) and then a three-row legend for reading it, which is a guide rather than a verdict on yours. Every row of that table is read at the last plotted point, but on this chart the limits are straight, so those numbers are the limits for every point. That is true of any attribute chart whose denominator does not vary, and of any chart drawn with Force Straight Limits on. 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. A split chart adds a Per-Split Breakdown block. There is no capability block and no histogram.
When the analysis finishes, the Control Chart task pane opens on the right. See Task Pane.