Turn sampling plans into clear risk estimates today. See acceptance odds at critical defect levels. Download results instantly for audits, training, and improvement teams.
| Plan | n | c | LTPD (%) | Consumer Risk β |
|---|---|---|---|---|
| Tight plan | 125 | 2 | 5.0 | 4.77% |
| Balanced plan | 80 | 2 | 6.5 | 10.09% |
| Fast screening | 50 | 1 | 8.0 | 8.27% |
| High assurance | 200 | 3 | 4.0 | 3.95% |
| Low sampling | 32 | 0 | 3.0 | 37.73% |
Probability of acceptance for defect rate p:
Consumer risk β = Pa(LTPD). Producer risk α = 1 − Pa(AQL), when AQL is provided.
With lot size N, defectives D, and sample n:
Use this when sampling without replacement and the lot is not very large relative to the sample.
Consumer risk (β) is the probability that an acceptance-sampling plan still accepts a lot at the lot tolerance percent defective. When LTPD is 6%, β=0.10 means one in ten bad lots may pass. Lower β increases protection, but it usually requires larger samples or a smaller acceptance number. For example, with n=50 and c=1 at LTPD 8%, β may exceed 0.20, which is often unacceptable for critical defects. If you set c=0, the plan becomes zero-acceptance, and β drops quickly as n grows, but inspection effort and false rejects increase.
The operating characteristic curve plots defect rate on the x-axis and acceptance probability on the y-axis. A steep curve is desirable: high acceptance near AQL and low acceptance near LTPD. For a fixed c, increasing n shifts the curve down at higher defect rates, reducing β while also reducing acceptance at moderate defect levels. A practical check is to read Pa at AQL, mid-quality, and LTPD; the larger the separation, the better the discrimination power of the plan.
The binomial model assumes independent draws and is a good approximation when the lot is large compared with the sample. The hypergeometric model is exact for sampling without replacement from a finite lot. If N=500 and n=125, the finite-population effect is noticeable, so hypergeometric acceptance can differ from binomial estimates. When n is 10% of N, prefer hypergeometric.
Adding an AQL input converts the same plan into a producer-risk view. Producer risk (α) is the probability of rejecting a good lot at AQL, computed as 1−Pa(AQL). Many programs target α near 0.05 and β near 0.10, then tune n and c until both constraints are satisfied in the same plan.
Use β, 1−β, and expected defects in the sample to explain why the plan matches the severity of the defect and the cost of escape. If β is elevated, reduce c or increase n, then document the revised plan and OC behavior. Exported CSV and PDF outputs help support audits, training, and continuous improvement reviews.
β is the probability your plan accepts a lot at the chosen LTPD defect rate. It quantifies the chance a poor-quality lot reaches customers under that sampling rule.
Set LTPD to the defect level you consider unacceptable for the product or failure mode. It is often higher than AQL and aligned with safety, warranty cost, and regulatory expectations.
Use hypergeometric when you sample without replacement and the sample is a meaningful fraction of the lot, such as n ≥ 10% of N. It reflects finite-lot effects more accurately than binomial.
With a fixed acceptance number c, a larger sample is more likely to detect defects in a bad lot. That lowers the probability of seeing ≤ c defects, so acceptance probability at LTPD drops.
If you enter AQL, the calculator reports α = 1 − Pa(AQL), the chance a good lot is rejected. Lower α reduces false rejects but can increase β unless you adjust n and c.
Record n, c, LTPD, β, and any AQL/α values, then attach the exported CSV or PDF to the control plan. Include the model choice and assumptions so reviewers understand the risk basis.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.