u-Chart (Defects per Unit)
Chart Statistics
0.022
3.978
2.000
25
0
4.600
Sample size varies between subgroups, so control limits stair-step per point. The values above use the average sample size.
Data Input
Label: Column 1 | Defect Count: Column 2 | Sample Size: Column 3 — change these in Chart Options. Loaded with a sample dataset so you can see the chart straight away. Overwrite it with your own counts, or paste columns from Excel — the chart updates as you type.
What Is a u Chart?
A u chart is an attribute control chart that monitors defects per unit when the inspection area varies from subgroup to subgroup. Its centerline is ū, the average defects per unit, and every subgroup gets its own control limits — ū ± 3√(ū/n) — so the limits stair-step with the amount inspected.
Perhaps you inspect a different number of panels each day, or fabric rolls of different lengths. Since a larger inspection area naturally contains more defects, raw counts cannot be compared directly. Instead, the u chart plots a rate. The distinction mirrors the one between the np chart and the p chart: constant goes with raw counts, varying goes with rates.
Like the c chart, the u chart counts defects rather than defective units — a single unit can carry several defects, and all of them are counted. Defect data follows the Poisson distribution, because you are counting occurrences within a defined area of opportunity.
The u Chart Formula and a Worked Example
Example dataset: over 10 days we inspected panels, and this time each single panel is one inspection unit, but the daily quantity varied between 3 and 6 panels depending on production. In total, we inspected 45 panels and recorded 90 defects. On day 2, we inspected 5 panels and found 12 defects.
u Chart Formulas and Calculation
- Plotted point (u): defects found that day ÷ units inspected that day. For the 5-panel day 2: u = 12 ÷ 5 = 2.4 defects per panel.
- Centerline (ū): total defects across all subgroups ÷ total inspection units across all subgroups = 90 ÷ 45 = 2 defects per panel. Do not average the daily rates, because that would give equal weight to subgroups covering different amounts of inspection.
- Control limits: ū ± 3√(ū/n), where n is the number of units in that subgroup. Just like the p chart, n sits inside the formula, so each subgroup gets its own limits. For day 2: 2 ± 1.897, giving a UCL of 3.90 and an LCL of 0.10 defects per panel.
The plotted point of 2.4 sits comfortably inside those limits, so day 2 is in control. Apply the same calculation to every other day to complete the u chart. These limits follow the standard Shewhart approach documented in the NIST/SEMATECH e-Handbook.
| Element | Formula / Result |
|---|---|
| Plotted point (u) | Defects ÷ units inspected = 12 ÷ 5 = 2.4 |
| Centerline (ū) | Total defects ÷ total units = 90 ÷ 45 = 2 |
| Control limits | ū ± 3√(ū/n) = 2 ± 1.897 (for n = 5) |
| Upper / lower control limit | 3.90 / 0.10 (recalculated per subgroup) |
Using the u Chart Maker
Everything you need is on this page — no installation and no account to try it. The chart type is already set to u-chart, so you can type your counts into the spreadsheet above or paste them straight from Excel or Google Sheets. The layout uses three columns:
- Labels: the subgroup names shown along the x-axis.
- Defect count: the total number of defects found in that subgroup.
- Sample size: the number of inspection units covered — panels, metres, boards. Unlike the c chart, these values do not have to be identical, and that is exactly the point of the u chart.
Open Chart Options to change which columns hold which values, or to adjust the display and filters. Signing in unlocks the full Attribute Chart module, where you can save studies and reload them later.
How to Interpret a u Chart
Notice that the control limits are not straight lines — they stair-step from point to point, because each subgroup has its own limits calculated from its own inspection size. Smaller inspection areas get wider limits and larger ones get tighter limits. The statistics panel reports the limits at the average sample size.
A point beyond a control limit signals special cause variation and is worth investigating — a machine may have drifted, a material lot changed, or a new operator taken over. You can strengthen detection further by applying the Western Electric Rules. On attribute charts, a point below the lower control limit can actually be good news, because it may indicate genuinely improved quality — but always verify it is not an inspection error. Finally, collect at least 20 to 25 subgroups before you rely on your control limits.
Frequently Asked Questions
What is a u chart used for?
A u chart is used to monitor defects per unit when the inspection area varies from subgroup to subgroup — for example, a different number of panels inspected each day, or fabric rolls of different lengths. Because it plots a rate rather than a raw count, subgroups of different sizes stay comparable. It is one of the four attribute control charts, alongside the np, p, and c charts.
What is the difference between a u chart and a c chart?
A c chart requires a constant inspection unit size, meaning the same area, length, or count of opportunities each time, while a u chart normalizes the defect count by the actual inspection unit size, so it works even when the amount inspected varies — for example, checking a different length of cable or a different number of panels each time.
What is the formula for u chart control limits?
The plotted point is u = defects ÷ units inspected in that subgroup, and the centerline is ū = total defects across all subgroups ÷ total inspection units across all subgroups. The control limits are ū ± 3√(ū/n), where n is the number of units in that subgroup. Because n sits inside the formula, each subgroup gets its own limits. If the lower limit calculates below 0, it is set to 0.
Why are the control limits on a u chart not straight lines?
The control limits step up and down because each subgroup covers a different amount of inspection area, and its limits are recalculated individually. Since the limit width depends on the square root of ū/n, smaller inspection areas widen the limits and larger ones tighten them. This stair-step appearance is normal and expected whenever the inspection size varies — it mirrors what happens on a p chart.
What is the difference between a u chart and a p chart?
Both handle varying subgroup sizes, but they count different things. A p chart plots the proportion of units that failed as a whole, based on the binomial distribution, so its values can never exceed 1. A u chart plots defects per unit, based on the Poisson distribution, and can exceed 1 because a single unit may carry several defects.
How much data do you need for a u chart?
Aim for at least 20 to 25 subgroups before you rely on the control limits, and size your subgroups so you expect roughly five or more defects in each. Below that, the normal approximation behind the three-sigma limits starts to break down. Very small inspection areas also produce very wide limits, which can make the chart insensitive to real shifts.
Do attribute control charts require normally distributed data?
No. The u chart’s limits come from the Poisson distribution, and the np and p charts’ limits from the binomial — not from the normal. The normal enters only as an approximation behind the three-sigma limits, which is exactly why the guidance is to keep expected counts at roughly five or more per subgroup.
Final Thoughts
The u chart is the most flexible of the two defect charts, and the right one whenever the amount you inspect changes between subgroups. When your inspection unit is genuinely fixed, the simpler c Chart Maker is easier to read. If you are counting failed units rather than individual flaws, use the np Chart Maker for a constant sample size or the p Chart Maker for a varying one. An overview of all four sits on the Attribute Control Chart Maker page.