A c-chart tracks the count of defects in a constant-size inspection unit, while a u-chart tracks defects per unit when the amount inspected varies from sample to sample. Both are attribute control charts built on the Poisson distribution, and both answer the same question: is my defect rate stable, or has something changed? Pick the wrong one and your control limits end up too tight or too loose, so you either chase ghosts or miss real shifts. This guide covers the statistical basis, the formulas, and a worked example with real numbers.
The c chart vs u chart question only arises when you are counting defects, so start by separating two words that get mixed up on the shop floor. A defect is a single nonconformity: one scratch, one missing solder joint, one pinhole in a coating. A defective is a whole unit that fails inspection, however many individual defects it carries. C-charts and u-charts count defects; p-charts and np-charts classify defectives. One painted panel can carry five defects, so counting defects preserves information that a simple pass or fail label throws away. All four belong to the attribute chart family within statistical process control, used when you count events rather than measure a continuous dimension.
Both charts assume defect counts follow a Poisson distribution, which fits when four conditions hold:
The Poisson property that makes the math simple is that variance equals the mean. The standard deviation of a defect count is just the square root of the average count, so three-sigma limits fall straight out of the center line with no separate range chart needed.
Use a c-chart when every sample exposes the same area of opportunity: one control cabinet, one PCB of a fixed design, ten square meters of fabric, one crate of 24 bottles. The formulas:
Because the inspection area never changes, the limits are two flat lines, which makes c-charts easy to maintain on a whiteboard right at the line.
When the amount inspected changes between samples (for example, you inspect everything a shift produces and shifts produce different quantities), raw counts stop being comparable. Twelve defects across 8 panels and twelve defects across 30 panels describe very different processes. The u-chart normalizes to defects per unit:
Because n sits inside the limit formula, the limits step up and down with each sample: small samples get wide limits, large samples get tight ones. Many practitioners use the average n whenever individual sample sizes stay within about 25 percent of that average, which restores flat limits at a small cost in accuracy.
A coatings line paints steel enclosure panels, and quality inspects for pinholes, runs, and inclusions.
C-chart scenario. Inspectors check exactly one reference panel per shift. Over 25 shifts they log 150 defects, so c-bar = 150 / 25 = 6.0 defects per panel. The standard deviation is sqrt(6.0) = 2.45, so UCL = 6.0 + 3 x 2.45 = 13.35, and since 6.0 - 7.35 is negative, LCL = 0. A shift logging 14 defects on its reference panel breaks the upper limit and triggers investigation; 13 does not.
U-chart scenario. The plant moves to 100 percent inspection, but output varies by shift. Over 20 shifts, inspectors check 400 panels and log 520 defects, so u-bar = 520 / 400 = 1.30 defects per panel. For a slow shift of 8 panels, the limits are 1.30 plus or minus 3 x sqrt(1.30 / 8) = 1.30 plus or minus 1.21, giving UCL = 2.51 and LCL = 0.09. For a busy shift of 32 panels, 3 x sqrt(1.30 / 32) = 0.60, giving UCL = 1.90 and LCL = 0.70. Note the effect of sample size: a rate of 2.50 defects per panel sneaks under the limit on the 8-panel shift (2.50 < 2.51) but signals loudly on the 32-panel shift. Small samples simply cannot separate moderate rate changes from noise.
The decision rule is short: constant inspection area, use a c-chart; varying area or quantity, use a u-chart. Then avoid the mistakes that quietly invalidate attribute charts:
Control charts are only as good as the data feeding them. Fabrico is an EU-built platform with EU data residency that gives factories the real-time data foundation behind quality work: live OEE and production monitoring, with computer vision that reads machine behavior even on equipment without a PLC. When a c-chart or u-chart flags a special cause, the loop closes in Fabrico's CMMS: raise a work order, assign the fix, log the root cause against the asset, and schedule the preventive task so the same defect source does not return. Quality signals stop dying in spreadsheets and start driving maintenance and process action inside one system.
Yes. With constant n, a u-chart carries exactly the same information as a c-chart; it simply divides every count by n. Many teams standardize on u-charts so the method survives future changes in inspection quantity, while the c-chart remains the simpler choice when the inspection unit truly never changes.
Large enough that the average defect count per sample is at least about five. Below that, the Poisson distribution is so skewed that the lower limit collapses to zero and the chart loses power to confirm improvements. If single panels average 0.5 defects, define the inspection unit as ten panels instead.
That is overdispersion, common when defects cluster or when between-day sources of variation act on the rate itself. Classic c and u limits will then produce constant false alarms. Laney's u'-chart, which widens the limits by an estimate of the extra variation, is the standard remedy.
Ready to run your defect charts on live production data instead of end-of-week spreadsheets? Book a Fabrico demo and see real-time monitoring and CMMS workflows on your own lines.
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