c-Chart (Count of Defects)
Chart Statistics
1.608
22.392
12.000
25
0
1.000
Data Input
Label: Column 1 | Defect Count: Column 2 — 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 c Chart?
A c chart is an attribute control chart that monitors the total count of defects per inspection unit, where the inspection unit stays constant. Its centerline is c̄, the average number of defects per inspection unit, with control limits at c̄ ± 3√c̄.
The c chart counts defects, not defective units — a single unit can carry several defects, and all of them are counted. That is what separates it from the np chart, which asks only whether each unit passed or failed. Defect data follows the Poisson distribution, because you are counting occurrences within a defined area of opportunity.
An important point: the inspection unit does not have to be a single item. It might be one painted door panel, but it could just as well be a group of 10 circuit boards inspected together, 5 metres of fabric, or a batch of 50 invoices. You define the inspection unit however it makes sense for your process. What matters is that the area of opportunity for defects is the same every time — if your inspection unit is 10 circuit boards, it must be 10 circuit boards in every subgroup. When it varies, you need the u chart instead.
The c Chart Formula and a Worked Example
Example dataset: we define the inspection unit as a group of 20 painted panels. Every day for 10 days we inspected 20 panels, counting every defect, including scratches, runs, and inclusions. Across the 10 days, we recorded 120 total defects.
c Chart Formulas and Calculation
- Centerline (c̄): total defects ÷ number of inspection units. Be careful: the number of inspection units is not the total number of panels. Each day we inspected one inspection unit (the group of 20 panels), so over 10 days we have 10 inspection units, not 200 panels. c̄ = 120 ÷ 10 = 12 defects per inspection unit.
- Control limits: c̄ ± 3√c̄. The c chart is based on the Poisson distribution, where the variance equals the mean, which is why c̄ simply appears under the square root. 12 ± 10.39 gives a UCL of 22.39 and, this time, a positive LCL of 1.61.
Done: centerline at 12, upper limit at 22.39, lower limit at 1.61, with the total defect count of each daily group plotted. A day with 23 or more defects signals that the painting process has shifted, and because the lower limit is positive here, a day with only 1 defect would also be an out-of-control signal. If your inspection unit were a single panel instead of a group of 20, you would apply exactly the same formulas. These limits follow the standard Shewhart approach documented in the NIST/SEMATECH e-Handbook.
| Element | Formula / Result |
|---|---|
| Centerline (c̄) | Total defects ÷ inspection units = 120 ÷ 10 = 12 |
| Control limits | c̄ ± 3√c̄ = 12 ± 10.39 |
| Upper control limit (UCL) | 22.39 |
| Lower control limit (LCL) | 1.61 (positive, because c̄ > 9) |
Using the c Chart Maker
Everything you need is on this page — no installation and no account to try it. The chart type is already set to c-chart, so you can type your counts into the spreadsheet above or paste them straight from Excel or Google Sheets. The layout uses two columns:
- Labels: the subgroup names shown along the x-axis.
- Defect count: the total number of defects found in that inspection unit. No sample-size column is needed, because the inspection unit is constant by definition — that constancy is the c chart's defining requirement.
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 c Chart
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, which flag non-random patterns even when every point stays inside the limits.
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. This matters more on the c chart than on most attribute charts, because its lower limit turns positive as soon as c̄ exceeds 9, so low-defect subgroups can genuinely signal. Finally, keep in mind that attribute charts need larger datasets than these training examples: collect at least 20 to 25 subgroups before you rely on your control limits.
Frequently Asked Questions
What is a c chart used for?
A c chart is used to monitor the total number of defects found in a constant inspection unit over time — for example, scratches per painted panel or solder faults per board. It shows whether the defect count is stable and flags any subgroup affected by a special cause. It is one of the four attribute control charts, alongside the np, p, and u charts.
When should you use a c chart vs. a u chart?
Use a c chart when you count defects within a constant inspection unit, and a u chart when the inspection area varies from subgroup to subgroup. The c chart plots the raw defect count, while the u chart plots defects per unit so counts from different inspection areas remain comparable.
What is the formula for c chart control limits?
The control limits for a c chart are c̄ ± 3√c̄, where c̄ is the average number of defects per inspection unit — total defects divided by the number of inspection units. The c chart is based on the Poisson distribution, where the variance equals the mean, which is why c̄ appears directly under the square root. If the lower limit calculates below 0, it is set to 0.
Does a c chart have to use a single item as the inspection unit?
No. The inspection unit can be any defined area of opportunity: one painted door panel, a group of 10 circuit boards inspected together, 5 metres of fabric, or a batch of 50 invoices. What matters is that the area of opportunity is identical every time — if your inspection unit is 10 circuit boards, it must be 10 circuit boards in every subgroup.
What is the difference between an np chart and a c chart?
An np chart counts defective units (each unit is pass or fail) with a constant sample size, using the binomial distribution. A c chart counts defects — a single unit can carry multiple defects — within a constant inspection area, using the Poisson distribution. Use np when a unit either passes or fails as a whole; use c when you're tallying flaws that can occur more than once per unit.
Can a c chart have a lower control limit above zero?
Yes, and it often does. Because the limits are c̄ ± 3√c̄, the lower limit becomes positive once c̄ exceeds 9. With c̄ = 12, for example, the LCL is 1.61, so a subgroup with only one defect is an out-of-control signal — which may mean genuine improvement worth understanding, or an inspection that missed defects.
How much data do you need for a c chart?
Aim for at least 20 to 25 inspection units before you rely on the control limits, and choose an inspection unit large enough that you expect roughly five or more defects in each. Below that, the normal approximation behind the three-sigma limits starts to break down and the chart loses its ability to signal reliably.
Final Thoughts
The c chart is the simplest of the two defect charts, and the right one whenever your area of opportunity is genuinely fixed. When the amount you inspect changes from subgroup to subgroup, switch to the u Chart Maker. 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.