Acceptance Sampling Calculator
For a single sampling plan — inspect n items, accept the lot if no more than c are defective — the probability of accepting a lot with a given defect rate, the average outgoing quality, and the inspection the plan really costs.
A sampling plan is a bet: draw n items, count the defects, accept if the count is at most c.
How the acceptance sampling calculator works
A sampling plan is a bet: draw n items, count the defects, accept if the count is at most c. The chance of accepting depends on the lot's true defect rate through the binomial distribution, and plotting it against the rate gives the operating characteristic curve. The producer's risk is a good lot rejected; the consumer's risk is a bad lot accepted.
Average outgoing quality is what the customer actually sees after rejected lots are screened, and it peaks at a defect rate the plan handles worst.
Formula: P_a = Σ_{k=0}^{c} C(n,k) p^k (1−p)^(n−k); AOQ = P_a × p × (N − n) / N; ATI = n + (1 − P_a)(N − n)
Worked examples
| Inputs | Probability of accepting the lot | Note |
|---|---|---|
| n = 125, c = 3 on a 2% lot | 75.867% | accepted three times in four |
| A good lot | 99.625% | almost always passes |
| A bad lot | 5.389% | almost always fails |
FAQFrequently asked questions
What is acceptance sampling?
Judging a whole lot from a sample: inspect n, accept if at most c are defective. It trades inspection cost against the risk of a wrong decision, and standards like ISO 2859 tabulate the plans.
What are the producer's and consumer's risks?
The producer's risk is a good lot — at the acceptable quality level — being rejected; the consumer's risk is a bad lot, at the lot tolerance rate, being accepted. Plans are chosen to hold both to about 5 and 10%.
What is average outgoing quality?
The defect rate the customer sees after rejected lots are fully screened and cleaned. It rises with the incoming rate, peaks, then falls as more lots get screened.
Why the binomial rather than hypergeometric?
The binomial is exact for sampling with replacement and very close without it when the sample is under a tenth of the lot. Above that the hypergeometric is slightly stricter.
Is c = 0 a good plan?
It is strict on the producer — a single defect rejects — and gives a steep curve. Zero-acceptance plans are common where any defect is unacceptable, at the cost of rejecting good lots.
Where these figures come from
- Nakajima (1988) — Introduction to TPM — the origin of Overall Equipment Effectiveness and its six big losses
- Health and Safety Executive — the UK workplace safety regulator
Last checked: September 2026. Definitions follow standard operations-management practice; where plants commonly differ, the page says so.