U Chart (Defects Per Unit)
Monitor defects per unit when the size of your inspection area changes from sample to sample. The U chart normalizes the defect count to a per-unit rate and adjusts its control limits to each sample's size.
Create U Chart →What is a U Chart?
A U chart is an attribute control chart that monitors the number of defects per unit when the inspection area or sample size varies. Like the C chart, it counts defects, the individual nonconformities, but instead of a raw count it plots the defect rate per unit, which makes samples of different sizes comparable.
This normalization is what lets the U chart handle variable inspection areas. Because the defect count is divided by the size of the area inspected, and larger areas offer more opportunity for defects, the control limits are recalculated for each sample based on its size, giving the U chart varying limits like the P chart.
The U chart is based on the Poisson distribution, appropriate for counts of defects. It is the variable-area counterpart of the C chart: use the C chart when the inspection unit is a constant size, and the U chart when it changes. It answers whether the defect rate per unit is in statistical control.
In plain terms: Like a C chart (counting flaws), but for when the thing you inspect isn't always the same size, one batch is 10 metres of fabric, the next is 15. The U chart converts to defects per unit so the sizes are comparable, and moves its control limits to match each sample's size.
Key Points
Defects Per Unit
Plots the defect rate per unit rather than a raw count, making samples of different sizes comparable.
Variable Inspection Area
Handles changing inspection areas by recalculating control limits for each sample, giving varying limits.
Poisson Basis
Based on the Poisson distribution, appropriate for counts of defects per unit of opportunity.
Key Formulas
Reading the Chart
Because the limits depend on each sample's inspected size, they step in and out along the chart, narrower for larger samples. A point beyond its own limits, or a non-random pattern, signals a special cause affecting the defect rate.
The U chart plots a rate, defects per unit, which keeps varying sample sizes comparable. If the inspection area is actually constant, the simpler C chart, plotting raw counts with flat limits, is preferable. And as always, the U chart counts defects, not defective units.
Assumptions & Validation
Counting Defects
Individual defects are counted, and a unit may have several.
If violated: To classify units as defective or not, use a P or NP chart.
Variable Inspection Area
The size of the inspection area varies between samples.
If violated: If the area is constant, the C chart is simpler.
Independent, Rare Defects
Defects occur independently, matching the Poisson model.
If violated: Address clustering or dependence between defects.
⚠️ Check assumptions first
The U chart is the variable-area counterpart of the C chart: both count defects using the Poisson distribution, but the U chart plots defects per unit and recalculates limits for each sample's size. Use it when the inspection area varies; if the area is constant, the C chart is simpler. And like the C chart, it counts defects, not defective units, so for pass/fail classification of whole units a P or NP chart is correct.
When NOT to Use U Chart
Constant Inspection Area
When the inspection unit is a constant size, the C chart is simpler with its flat limits.
Counting Defectives
To classify units as defective or not, use a P chart (variable size) or NP chart (constant size).
Continuous Data
For measured variable data, use an X-bar R, X-bar S or XmR chart.
Industry Applications
Variable-Size Inspection
Monitor defects per unit when samples cover different areas, lengths or quantities.
Textile & Material Defects
Track flaws per square metre or per length when roll sizes vary.
Process Control
Detect shifts in the defect rate of a stable process with variable sampling.
Error Rate Monitoring
Track errors per unit across documents or batches of differing size.
Frequently Asked Questions
What is a U chart used for?
A U chart monitors the number of defects per unit when the inspection area or sample size varies between samples. It counts defects, the individual nonconformities, and plots them as a per-unit rate so that samples of different sizes are comparable. Based on the Poisson distribution, it determines whether the defect rate per unit is in statistical control, and it is the variable-area counterpart of the C chart.
What is the difference between a C chart and a U chart?
Both count defects using the Poisson distribution, but a C chart is used when the inspection unit is a constant size, plotting the raw defect count with flat control limits, while a U chart is used when the inspection area varies, plotting defects per unit with control limits that adjust to each sample's size. The choice depends on whether the area of opportunity for defects is constant or variable.
What is the difference between a U chart and a P chart?
A U chart counts defects per unit using the Poisson distribution, where a single unit can have several defects. A P chart counts defective units as a proportion using the binomial distribution, where each unit is simply defective or not. Both handle variable sample sizes with adjusting limits, but they differ in the fundamental distinction of defects versus defectives, flaws counted versus units classified.
Why do the control limits vary on a U chart?
The control limits of a U chart depend on the size of each sample's inspection area, because a larger area offers more opportunity for defects and gives a more precise estimate of the rate. Larger samples produce narrower limits and smaller samples wider limits. When the inspected size varies between samples, the limits are recalculated for each, producing a stepped appearance similar to the P chart.
What distribution is the U chart based on?
The U chart is based on the Poisson distribution, which models counts of rare, independent events in a defined interval of opportunity. Because it plots defects per unit, the Poisson rate is divided by the sample size in the control limit formula. The Poisson basis assumes defects occur independently, so clustering or dependence between defects can undermine the chart's validity.
When should I use a U chart instead of a C chart?
Use a U chart when the size of the inspection area changes from sample to sample, since it normalizes to defects per unit and adjusts its limits accordingly. Use a C chart when the inspection unit is always the same size, because it can plot raw counts with simpler flat limits. If sample sizes vary and you used a C chart, the constant limits would be invalid, which is why the U chart exists.
Monitor Defect Rate With Varying Samples
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