u Chart
The u chart is an attribute chart in SPC Chart PRO that monitors defects per unit when the size of the inspected area varies from sample to sample.
The u chart is to the c chart what the p chart is to the np chart: it counts defects (a unit can carry several) under the Poisson distribution, but instead of assuming a fixed inspection area it divides the defect count by the number of units inspected, giving a rate. That lets you chart samples of different sizes together — 10 boards one hour, 25 the next — because a rate of 0.4 defects per board means the same thing regardless of how many boards were in the sample.
Select u chart (defects per unit) in the Chart Type dropdown.
How It Works
Each row of your query is one sample. The value field holds the total defect count for that sample, and a second column (or a fixed option) gives the number of units inspected. The panel plots defects ÷ units — the defect rate.
The center line is the overall defect rate, pooled across the samples included in estimation. The control limits are set at three standard deviations from the center line under the Poisson distribution, and because the Poisson standard error shrinks as the inspected area grows, the limits step in and out to follow each sample's own size.
Enable Nelson run rules to flag patterns in the defect rates.
Setting It Up
In the SPC section, with the u chart type selected:
| Option | Description |
|---|---|
| Sample size field | A numeric field in your query giving the number of units inspected per sample. It is hidden from the plot automatically. |
| Fixed sample size | A constant number inspected per sample, used when no sample-size field is selected. |
Rows with a missing or negative count, or a missing or non-positive sample size, are treated as gaps: they are not plotted and do not contribute to the center line or the limits.
Variable Control Limits
When the inspected area varies, the limits vary with it — larger samples give tighter limits — and the panel draws them as stepped lines that follow each sample's own limit.
The scalar LCL/UCL shown in labels, the statistics table, and the fill region are representative values computed from the average sample size. Run rules derive sigma from each point's upper limit rather than these representative values.
Methods and Formulas
Let each sample i contribute cᵢ defects over nᵢ units inspected.
| Quantity | Formula |
|---|---|
| Plotted value | uᵢ = cᵢ ⁄ nᵢ |
| Center line | ū = Σcᵢ ⁄ Σnᵢ |
| Control limits | ū ± 3·√( ū ⁄ nᵢ ) |
The lower limit is floored at 0.
Classic u limits use Poisson assumptions. If the observed variation exceeds the Poisson prediction (overdispersion), the limits may be too narrow, especially with large samples. Consider a Laney u′ chart when overdispersion explains the excess variation.
Choosing the u Chart
| Scenario | Chart |
|---|---|
| Counting defects, inspected area varies | u |
| Counting defects, inspected area fixed | c |
| u chart with large samples and limits that look too tight | Laney u′ |
The sample-size configuration and chart type are saved with the dashboard. Like every chart type, the u chart works with both a time and a numeric X-axis.
The u chart is part of SPC Chart PRO. See requirements, licensing, and support.