c Chart Calculator — Defects per Constant Inspection Unit
Paste a column of defect counts and get the c chart: centre line c̄, limits c̄ ± 3√c̄, the point exactly on the limit left unflagged the way the convention says, and an honest note when your counts are too low for the normal approximation those limits rest on.
When a c chart is the right chart, and when it is the u chart
A c chart counts DEFECTS — nonconformities — in a fixed area of opportunity. One wafer, one weld, one roll of coated film, one hundred metres of pipe: whatever the unit is, it has to be the same unit every time. If it is, the count itself is the statistic and the limits are one flat pair.
The moment the area of opportunity varies — twelve panels this shift and twenty the next, a 40 m length and a 90 m length — a c chart is the wrong instrument, because a bigger area is expected to contain more defects for reasons that have nothing to do with the process. That is the u chart: it divides by the size to get defects per unit, and then has to recompute the limits at every point, because a subgroup with more evidence in it deserves a tighter limit. Paste varying sizes into this page and it will say so rather than quietly averaging them away.
The other fork is p and np. Those count defective ITEMS out of a fixed number inspected, so their count can never exceed the number examined and the distribution is binomial. A c chart is Poisson: one item can carry six defects, and nothing caps the count.
Data
Paste straight from Excel, Minitab or a CMM export — include the header row and the columns are matched by name, in any order.
| # | Sample(opt) | Defects | Units inspected(opt) | |
|---|---|---|---|---|
| 1 | ||||
| 2 | ||||
| 3 | ||||
| 4 |
0 rows of data
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Enter data on the left to chart it
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Options
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How the limits are computed
c̄ is the total number of defects divided by the number of samples. Under a Poisson process the variance equals the mean, so σ = √c̄, and the limits are c̄ ± 3√c̄. That is the whole calculation, and it is worth noticing what is missing from it: nothing about the spread of your data enters anywhere. σ is derived from the centre line and the assumed distribution, not estimated from the observations.
Which is why this tool runs a χ² index of dispersion over your counts and prints the result when it fails. If the counts vary much more than a Poisson process allows — clustering, mixed product, an inspector effect, or a real shift part-way through — then √c̄ is too small, every limit is too narrow, and the chart will flag ordinary behaviour. There is no sigma estimator to absorb that, so the only honest response is to say so on the figure.
Two things about these limits that are easy to get wrong
A point exactly on the limit is not a signal. Out of control means strictly beyond. The NIST worked example this page loads by default is the cleanest demonstration of it in print: sample 3 has 28 defects against an upper limit of exactly 28 and is not flagged, and sample 24 has 31 and is. Two implementations that disagree about this report different numbers of signals on the same data.
Below c̄ = 9 there is no lower control limit at all, and that is arithmetic rather than a rule somebody made up: c̄ − 3√c̄ is positive only when c̄ exceeds nine. The consequence matters more than the fact. With no lower limit, a genuine improvement in the process cannot be detected by the limit alone, and the run rules that work in the zones below the centre line cannot fire either. This tool suppresses those tests and names them, rather than reporting them as passed.
When the counts are too low for the normal approximation
The 3σ limits are a normal approximation to a Poisson count, and the handbook this page reproduces puts the floor for that approximation at a mean of five. Below it the limits still draw and they are still roughly right, but their tail areas are not the nominal 0.135 % a side: NIST’s own worked figure is that at a mean of 10 the true probability below the lower limit is about a thirtieth of the assumed one.
The alternative is to plot a variance-stabilising transform of the count instead, with limits at ȳ ± 3 on the transformed scale. Three are offered, all as the handbook prints them, with its attributions: 2√c, 2√(c + 3/8), and √c + √(c+1). The axis then reads in transformed units, which is unfamiliar, so the figure also prints the limits converted back to counts — a transform is a change of scale, not a change of answer, and you should be able to check it.
Common questions
- What is the difference between a c chart and a u chart?
- The area of opportunity. A c chart assumes every sample covered the same amount of product and plots the raw count; a u chart divides by the amount inspected and plots defects per unit, which forces the control limits to be recomputed for every point. If your inspection size is constant the two charts say exactly the same thing; if it varies, only the u chart is correct.
- Why is there no lower control limit on my c chart?
- Because c̄ − 3√c̄ came out negative, and a defect count cannot be. That happens for any c̄ of nine or less. The chart draws without one and says so, and it also suppresses the run rules that need the zones below the centre line, because those tests cannot fire for a reason that has nothing to do with your process.
- A point is sitting exactly on the control limit. Is it out of control?
- No. The convention is strictly beyond the limit, and this tool follows it. The dataset that loads by default contains exactly this case, so you can see the answer rather than take it on trust.
- What is the difference between a defect and a defective?
- A defective is an item that failed; a defect is one thing wrong with it. A door with three scratches is one defective and three defects. Count defectives and you want a p or np chart, which is binomial; count defects and you want a c or u chart, which is Poisson and has no upper bound on the count.
- Is my data uploaded anywhere?
- No. The whole calculation runs as JavaScript in this browser tab, and nothing on this site accepts a measurement — the only server code here takes a payment. That is why the tool is usable on data you are contractually barred from putting in a cloud service.