OC Curve (Operating Characteristic)
A graph showing the Probability of Acceptance (Pa) of a lot as a function of the actual defect rate (p). The steeper the curve, the more discriminating the sampling plan — it better separates good lots from bad ones.
Pa ↑
100% ┤╲ AQL zone (Pa ≥ 95%)
95% ┤ ╲
┤ ╲
10% ┤ ╲ LQ zone (Pa ≤ 10%)
0% ┼────────────── p →
Pa — Probability of Acceptance
The probability that a lot with a given defect rate p will be accepted by the sampling plan. Calculated using Poisson approximation (λ = n·p < 10) or Binomial distribution.
Pa = P(X ≤ Ac | n, p)
Where Ac is the acceptance number, n is sample size, and X is the number of defects found.
AQL — Acceptable Quality Level
The maximum defect rate (%) that is considered acceptable. At the AQL level, the sampling plan should accept the lot with high probability (typically Pa ≥ 95%). AQL protects the producer: good lots should rarely be rejected.
Target: Pa(AQL) ≥ 95%
LQ — Limiting Quality
The defect rate (%) at which the lot is considered unacceptable. At the LQ level, the plan should reject the lot with high probability (Pa ≤ 10%). Conventionally estimated as LQ = 5 × AQL in this calculator.
Target: Pa(LQ) ≤ 10%
α — Producer's Risk
The probability of rejecting a good lot — a lot whose actual defect rate equals the AQL. A Type I error. Ideally α ≤ 5%.
α = 1 − Pa(p = AQL)
High α means good lots are frequently sent back to the supplier unnecessarily, increasing costs.
β — Consumer's Risk
The probability of accepting a bad lot — a lot whose actual defect rate equals the LQ. A Type II error. Ideally β ≤ 10%.
β = Pa(p = LQ)
High β means defective lots slip through to the production line or end customer.
Defect Classifications
Critical: Defects that could cause hazard, safety risk, or regulatory non-compliance. Zero tolerance is standard (Ac = 0).
Major: Defects likely to cause product failure or customer dissatisfaction. Low AQL (0.65%–1.5%).
Minor: Defects unlikely to affect function but deviate from specifications. Higher AQL (2.5%–6.5%).
How to Read the OC Curve
Pa = 100% when p = 0 (no defects → always accept).
Pa decreases as p increases — higher defect rate means lower chance of acceptance.
The dashed lines at Pa = 95% and Pa = 10% mark the AQL operating point and LQ operating point respectively.
Lower Ac produces a steeper curve — stricter plans discriminate better but increase α.
Distribution note: This calculator uses the Poisson approximation (Pa = e−λ Σ λx/x!) when λ = n·p < 10 and n ≥ 30 — standard for ISO 2859-1 sampling plans. The Binomial distribution is used otherwise for exact calculation. Both converge for large n and small p.