Learn · updated 2026-10-21
The p chart (fraction defective)
Use a p chart when each item either passes or fails and you track the fraction that fail in each sample. It works even when the sample size changes, because each sample gets its own limits.
The formulas. p̄ is the total defectives divided by the total inspected; nᵢ is the size of sample i.
CL = p̄UCL = p̄ + 3√(p̄(1 − p̄)/nᵢ)LCL = p̄ − 3√(p̄(1 − p̄)/nᵢ)
If the LCL comes out below 0, it is set to 0.
Worked example: NIST, 30 wafers of 50 chips
The NIST/SEMATECH e-Handbook lists the fraction of defective chips on each of 30 wafers, 50 chips per wafer. That is 347 defective chips out of 1,500.
- p̄ = 347 / 1500 = 0.2313.
- σ for n = 50: √(0.2313 × 0.7687 / 50) = 0.0596.
- Limits: 0.2313 ± 3 × 0.0596 → UCL 0.4102, LCL 0.0524.
- Wafers 15 and 23 (fractions 0.44 and 0.48) are above the UCL: two special-cause signals worth investigating.
p, np, c or u?
- p: fraction defective; sample size may vary.
- np: number defective; same sample size every time. Same signals as p, in counts.
- c and u: for defects (flaws), where one item can have several. See which chart to use.
With very large samples (thousands per point) the p chart's limits get so tight that almost every point looks out of control. That's overdispersion; a Laney p′ chart corrects for it.