What is the difference between a c-chart and a u-chart?

Both plot defect counts modeled by the Poisson distribution, but a c-chart requires a constant inspection unit and uses flat control limits, while a u-chart plots defects per unit and recomputes limits for each sample because the inspected area varies. Use c when every sample is the same size and u when the amount inspected changes.

What is the difference between a c-chart and an np-chart?

A c-chart counts defects, individual flaws, several of which can appear on one unit. An np-chart counts defective units, whole items that either pass or fail, in a constant sample size. Defects use c or u charts and follow the Poisson distribution; defectives use np or p charts and follow the binomial distribution.

How do you calculate c-chart control limits?

Compute c-bar, the average number of defects per inspection unit across your baseline samples. The center line is c-bar, the upper control limit is c-bar plus three times the square root of c-bar, and the lower control limit is c-bar minus three times the square root of c-bar, set to zero if that value is negative.

Why is the lower control limit on a c-chart often zero?

Because defect counts cannot be negative. When c-bar is small, the formula c-bar minus three times the square root of c-bar produces a negative number, which is impossible, so the lower limit is set to zero. The practical effect is that a low-count c-chart can only signal on the high side.

How many samples do you need to set up a c-chart?

A common baseline is 20 to 25 inspection units collected while the process is running normally, which gives a stable estimate of c-bar for the center line and limits. It also helps to keep the average count reasonably large, roughly five or more defects per unit, so the three-sigma limits approximate the skewed Poisson well.

What assumptions does a c-chart make?

It assumes defects follow a Poisson distribution: they occur independently, at a constant average rate, and are rare relative to the many places they could appear, all on a constant inspection unit. If defects cluster or one defect triggers others, the Poisson model understates variation and the chart over-signals.

C-Chart: Control Chart for Defect Counts

Q: What is a c-chart used for?

A c-chart tracks the number of defects (nonconformities) found in a fixed-size inspection unit over time, so you can tell a stable defect rate from a real change. It fits count-based and visual inspections such as paint blemishes per panel, weld defects per assembly, or solder defects per board, where each unit can carry several defects at once.

When you are counting flaws rather than sorting bad units, one statistic draws both limits, because the Poisson variance equals its mean.

A c-chart is an attribute control chart that plots the count of defects per inspection unit over time, using control limits derived from the Poisson distribution. It applies when the inspection unit (the area of opportunity) is constant, and its limits are the average defect count plus or minus three times the square root of that average. Because the Poisson standard deviation is the square root of the mean, the c-chart needs only one statistic, the average count, c-bar, to draw both limits.

The c-chart is the right tool when you are counting flaws, not sorting good parts from bad. Paint blemishes on a hood, solder defects on a board, weld porosity on a frame, typos on a printed page: each item can carry several defects at once, and the c-chart tracks the rate at which those defects appear. This guide covers when a c-chart fits, the Poisson math behind its limits, how to build and read one, and the mistakes that quietly invalidate it.

What is a c-chart used for?

A c-chart monitors the number of defects (nonconformities) found in a fixed-size inspection unit, sample after sample, so you can tell a stable defect rate from a real change. The defining condition is a constant area of opportunity: every inspection unit must offer the same chance for defects to occur. One car door, one square meter of fabric, one printed circuit board, one 100-meter roll, the unit is fixed, and you count how many defects land in it.

This is what separates the c-chart from its cousins. A control chart for attributes splits along two questions: are you counting defectives (whole units that pass or fail) or defects (individual flaws, several of which can sit on one unit)? And is the sample size constant or varying? Defectives go on p or np charts. Defects go on c or u charts. The c-chart is specifically defects with a constant inspection unit; when the inspected area changes size from sample to sample, you switch to a u-chart, which plots defects per unit and recomputes limits for each sample.

The c-chart lives in one cell: you are counting defects, and the inspection unit stays the same size every sample.

Why are c-chart limits based on the Poisson distribution?

Defect counts follow a Poisson distribution when defects occur independently, at a constant average rate, and are rare relative to the many places they could appear. Those conditions describe most defect-counting: a weld could have a flaw at thousands of points along its length, but only a few actually do, and one flaw does not make the next more likely. The Poisson distribution is the natural model for exactly that kind of "many chances, few hits" counting.

The Poisson distribution has one unusual property that makes the c-chart simple: its variance equals its mean. So if the average defect count is c-bar, the standard deviation is the square root of c-bar. Shewhart's three-sigma logic then gives the limits directly:

Center line (CL): c-bar, the average number of defects per inspection unit across your baseline samples.
Upper control limit (UCL): c-bar + 3√c-bar.
Lower control limit (LCL): c-bar − 3√c-bar, set to 0 whenever that formula goes negative, because a count of defects cannot be less than zero.

One consequence matters on the floor: when c-bar is small, the lower limit clamps at zero and the chart can only signal on the high side. That is fine for catching a worsening process, but it means a genuine improvement (a real drop in defects) is harder to detect statistically. It also means the Poisson is noticeably skewed at low counts, so the three-sigma limits are approximate. A common rule of thumb is to keep the average count reasonably large, roughly five or more defects per unit, so the limits behave well; if your counts are consistently near zero, enlarge the inspection unit or aggregate more area per sample.

How do you build a c-chart?

Building a c-chart is a five-step routine once you have fixed the inspection unit.

Define the inspection unit and hold it constant. Decide precisely what one sample is, one panel, one board, one 10-meter length, and make sure every sample is the same size. The unit is your area of opportunity, and the whole method depends on it not changing.
Collect a baseline of counts. Inspect and record the number of defects on each unit for a run of samples, commonly 20 to 25, taken while the process is running normally. Count every defect, not just whether the unit had any.
Compute c-bar. Add all the defect counts and divide by the number of inspection units. This average is both the center line and the seed for the limits.
Compute the control limits. UCL = c-bar + 3√c-bar; LCL = c-bar − 3√c-bar, floored at zero. These limits are horizontal because the inspection unit is constant.
Plot in time order and extend the limits forward. Draw the center line and limits, plot each count in sequence, and continue plotting new samples against the frozen baseline limits. Investigate any point outside the limits or any non-random pattern.

Worked numbers make it concrete. Suppose you inspect 20 painted panels and record a total of 60 defects. Then c-bar = 60 / 20 = 3.0 defects per panel. The square root of 3.0 is about 1.73, so UCL = 3.0 + 3(1.73) = 8.2 and LCL = 3.0 − 3(1.73) = −2.2, which floors to 0. A panel showing 9 defects sits above the 8.2 limit and signals; a panel showing 0 is well within the noise, since the chart cannot go below zero. (Note that at c-bar = 3 the counts are on the low side of the rule of thumb, so treat those limits as approximate and consider a larger inspection unit if signals are borderline.)

Twenty panels around a center line of 3. The single point above the upper limit is the signal; the lower limit rests on zero, so the chart only alarms upward.

How do you read a c-chart once it is running?

Read it the same way you read any Shewhart chart: a process in control looks like random scatter around the center line, inside the limits, with no patterns. A point beyond the upper control limit is the clearest signal, an inspection unit with far more defects than the process normally produces. The run-based patterns from the Western Electric rules still apply: a long run on one side of the center line, or a steady trend, points to a shift in the underlying rate even when no single point breaks the limit.

Three cautions are specific to c-charts. First, because the lower limit usually sits at zero, do not read "zero defects" as a special-cause improvement unless a run of zeros persists; a single clean unit is ordinary. Second, the c-chart assumes independence, if one defect tends to cause clusters of others (a contamination event, a torn tool leaving repeated marks), the Poisson model understates variation and the chart over-signals. Third, keep operational definitions tight: everyone counting defects must agree on what counts as one defect, or the chart tracks inspector disagreement instead of the process.

The Poisson math and where it comes from

The c-chart is old, standardized, and well documented. The numbers worth keeping straight:

The c-chart and its Poisson-based limits are documented in the NIST/SEMATECH e-Handbook of Statistical Methods which gives the counts-of-defectives and counts-of-defects charts and the three-sigma limit formulas (NIST/SEMATECH e-Handbook, 6.3.3.2).
Control charts originate with Walter Shewhart at Bell Telephone Laboratories in 1924, and the three-sigma limit is his economic choice balancing false alarms against missed signals (ASQ, Control Chart).
For a Poisson variable, variance equals the mean, so the standard deviation is √c-bar, the single fact that lets one statistic set both limits (ASQ).

Where the c-chart fits your quality system

The c-chart earns its keep on visual and count-based inspections that a variables chart cannot touch, surface finish, cosmetic defects, assembly flaws, documentation errors. It sits alongside the rest of statistical process control as the tool for "how many flaws," while p and np charts handle "how many bad units" and variables charts handle measured dimensions. When defect counts start climbing, the chart tells you when something changed; pairing it with a Pareto chart of defect types tells you what to chase first, and a rising rate that traces to a repeatable cause belongs in your defect tracking and nonconformance records rather than a quiet rework bin.

The bottleneck is rarely the arithmetic, it is capturing honest counts at the station. A c-chart drawn from tally marks on a clipboard is only as current as the last time someone typed them in. Digitizing the defect count at the point of inspection, the way Harmony's live capture and shop-floor visibility tooling does, means the chart updates itself and the counts stay searchable across shifts, feeding the same quality trends your review meetings already run. A c-chart is not the only sampling decision on a defect-counting line, either; when the question shifts from monitoring a process to accepting or rejecting a lot, the companion piece on c=0 sampling plans covers the acceptance side. The c-chart is one of the seven basic quality tools for a reason: it turns a pile of tally marks into a clear statement about whether your defect rate is holding steady or drifting.