Attributes Control Charts (p, np, c, u)
Also known as: p-chart, np-chart, c-chart, u-chart, nitelik kontrol kartı
Attributes control charts extend Shewhart's framework to count and proportion data — quality characteristics that are classified rather than measured. The p- and np-charts monitor the proportion or number of defective items using the binomial distribution, while the c- and u-charts monitor the number of defects per unit using the Poisson distribution. They are the standard statistical-process-control tools when inspection yields pass/fail or defect counts rather than continuous measurements.
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When to use it
Use attributes charts when inspection produces classifications or counts rather than measurements: fraction of defective parts, number of nonconformities per product, error counts per document, or defect rates in a service process. Choose p/np when classifying items as conforming or not, and c/u when counting defects that can occur multiple times per unit. They require adequate subgroup sizes so the normal approximation to the binomial or Poisson is reasonable (a common guideline is expected counts of at least about five), and they assume independence and a constant in-control rate within subgroups. When a continuous measurement is available, a variables chart (Shewhart X-bar/R, or CUSUM/EWMA for small shifts) is more informative and should be preferred.
Strengths & limitations
- Monitor quality when only pass/fail or defect-count data are available.
- Cover the common cases through four standard charts (p, np, c, u) with simple formulas.
- Handle varying subgroup sizes via point-specific limits (p- and u-charts).
- Integrate naturally with the broader Shewhart SPC framework and run rules.
- Less informative than variables charts, which use the full measurement rather than a classification.
- Rely on binomial/Poisson approximations that need adequately large counts to be valid.
- Insensitive to small shifts compared with CUSUM/EWMA approaches.
- Sensitive to violations of independence and to over-dispersion relative to the assumed distribution.
Frequently asked
When do I use a p-chart versus a c-chart?
Use a p-chart (or np-chart) when each inspected item is classified as defective or not and you track the proportion (or number) defective — a binomial situation. Use a c-chart (or u-chart) when you count the number of defects, which can be more than one per item — a Poisson situation. The key question is 'defective items' versus 'defects per item'.
What is the difference between p and np, or c and u?
p and np monitor the same thing on different scales: p is the fraction defective and np is the count defective, with np requiring a constant subgroup size. Similarly, c monitors defects in a fixed-size inspection unit while u monitors defects per unit and accommodates varying unit sizes via point-specific limits.
Why might my attributes chart give too many false alarms?
A common cause is over-dispersion: real count data are often more variable than the binomial or Poisson model assumes, so the standard three-sigma limits are too tight. Remedies include using a model that accounts for extra variation (e.g., beta-binomial or negative-binomial based limits) or widening the limits accordingly.
Sources
- Shewhart, W. A. (1931). Economic Control of Quality of Manufactured Product. D. Van Nostrand Company. ISBN: 978-0-87389-076-2
- Montgomery, D. C. (2009). Introduction to Statistical Quality Control (6th ed.). John Wiley & Sons. ISBN: 978-0-470-16992-6
How to cite this page
ScholarGate. (2026, June 2). Attributes Control Charts (p, np, c, u). ScholarGate. https://scholargate.app/en/statistics/attributes-control-chart
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- CUSUM ChartStatistics↔ compare
- EWMA ChartStatistics↔ compare
- Proportion TestStatistics↔ compare
- Shewhart Control ChartStatistics↔ compare