Try it while you read
Open the free Attribute Control Charts tool and click Load sample: it reproduces the case study below.
Theory: counting instead of measuring
Not every quality characteristic is measured. Visual inspection, leak tests or functional checks give a count: good or bad, number of defects. Attribute control charts apply the same idea as variables charts, telling common-cause from special-cause variation, to such counts.
| Chart | Counts | Sample size | Distribution |
|---|---|---|---|
| p | proportion of defective units | may vary | binomial |
| np | number of defective units | constant | binomial |
| c | number of defects | constant area or unit | Poisson |
| u | defects per unit | may vary | Poisson |
With variable sample sizes the limits change from sample to sample: larger samples get narrower limits because their proportion is estimated more precisely. To apply run rules consistently, the tool standardises the points.
Key point
Step by step
- Choose the chart type with the table above.
- Collect 20 to 30 samples, one per shift, day or lot.
- Enter count and sample size in the table, one row per sample.
- Read the chart: points beyond the limits and run rules flag special causes.
- Act: investigate each signal and, once the cause is removed, exclude it to calculate the limits for ongoing control.
Case study: final inspection of housings
Final inspection records the number of rejected housings per shift and the number inspected, for 20 shifts (the Load sample p chart).
- Average proportion defective p̄ = 5.99 %, upper limit about 11.1 %.
- Sample 8 is at 15.1 %, above its upper control limit: a special cause.
- All other shifts are between 3.8 % and 7.6 %, inside the limits.
The team finds that shift 8 ran with a new batch of castings with porosity. The batch is blocked, the supplier is informed through an 8D, and sample 8 is excluded when the limits are frozen. Because the remaining process still runs at about 6 % defective, a Pareto analysis of the defect types is started to reduce the level itself.
Result
Common mistakes
- Using an np chart with varying sample sizes.
- Treating a stable chart as “good”: stable at 6 % defective is still 60,000 PPM.
- Recalculating the limits every week, which hides gradual deterioration.
Frequently asked questions
p chart or np chart?
Both count defective units. The np chart plots the number and needs a constant sample size; the p chart plots the proportion and also works with variable sample sizes.
Can attribute charts replace a capability study?
They show stability and the average defect level, which can be converted to PPM. They are less sensitive than variables charts, so measured characteristics should use X-bar/R or I-MR charts where possible.