Define a single-sampling plan (n, c) and generate an OC curve over a defect-rate range.
Example probabilities for a common plan (n = 50, c = 1) using the large-lot model.
| Defect rate (%) | Pa | Interpretation |
|---|---|---|
| 0.50 | 0.9103 | High acceptance when defects are rare. |
| 1.00 | 0.7358 | Acceptance begins to drop as defects rise. |
| 3.00 | 0.1994 | Most lots are rejected at this quality level. |
| 5.00 | 0.0401 | Acceptance becomes unlikely for poor quality. |
| 8.00 | 0.0047 | Near-certain rejection at very high defects. |
Probability of acceptance (Pa) is the chance a lot is accepted under a sampling plan.
- Enter your sampling plan: sample size (n) and acceptance number (c).
- Select the curve model: large-lot or finite-lot, and add lot size if needed.
- Set the defect-rate range and step size to control curve resolution.
- Optionally enter AQL and LTPD to estimate producer and consumer risks.
- Press Submit to view the curve, table, and risk points above the form.
- Use Download CSV or PDF to save results for audits and reporting.
What an OC Curve Represents
An operating characteristic curve plots defect rate on the x-axis and probability of acceptance (Pa) on the y-axis for a single-sampling plan. A steep curve rejects poor quality quickly; a flatter curve accepts more lots across the range. For example, with n=50 and c=1, Pa might be about 0.736 at 1% defective, yet near 0.040 at 5% defective.
Inputs That Shape Plan Strictness
Sample size n and acceptance number c control the inspection burden and the rejection power. Increasing n generally lowers Pa at every defect level, while increasing c raises Pa by allowing more defects in the sample. If you change c from 1 to 2 with the same n, acceptance at moderate defect rates can increase substantially, shifting the curve upward.
Risk Interpretation at AQL and LTPD
Quality programs often specify an acceptable quality level (AQL) and a limiting tolerance percent defective (LTPD). The calculator estimates Pa at those points and converts them to risks: producer’s risk α = 1−Pa(AQL) and consumer’s risk β = Pa(LTPD). If Pa(AQL)=0.95, then α=0.05, meaning 5% of good lots could be rejected. If Pa(LTPD)=0.10, then β=0.10, meaning 10% of bad lots could slip through.
Binomial Versus Finite-Lot Modeling
When lots are large relative to the sample, the binomial model approximates selection with replacement and uses p as the defect probability. When the sample is a meaningful fraction of the lot, the hypergeometric model is better because it accounts for the exact number of defectives D in a finite lot of size N. With smaller N, Pa can differ noticeably at the same nominal percent defective, especially for larger samples.
Using the Curve to Set Policy
Use the chart and table to compare alternative plans before committing procedures. Choose a defect-rate range that covers typical process performance and potential worst cases. For audits, export the curve points to CSV, and keep the PDF report with the selected n and c. When requirements change, a quick re-run shows how inspection strictness and risk trade-offs move.
1) What is this calculator computing?
It computes the probability of accepting a lot across defect rates for a single-sampling plan. The curve helps you visualize how likely acceptance is at good, marginal, and poor quality levels.
2) How do n and c affect the curve?
Larger n usually lowers acceptance at the same defect rate because more items are inspected. Larger c raises acceptance because the plan tolerates more defects in the sample. Together they define the strictness of the plan.
3) When should I use the finite-lot option?
Use the finite-lot option when the sample is a meaningful fraction of the lot, such as n/N above about 5–10%. In that case, without-replacement effects matter and the hypergeometric model is more accurate.
4) How are producer and consumer risks shown?
Enter AQL and LTPD. The tool reports Pa at each point, then estimates producer’s risk as α = 1−Pa(AQL) and consumer’s risk as β = Pa(LTPD). These values summarize the plan’s trade-offs.
5) Why don’t my results match a handbook table?
Differences can come from rounding, using percent defective versus defect probability, finite-lot versus large-lot assumptions, or a different plan definition. Confirm n, c, N, and the exact defect rate points before comparing.
6) What’s the best way to export results?
Use CSV for full curve data that you can graph elsewhere, filter, or archive. Use the PDF report for a quick record of inputs, risk points, and a table snapshot for audits or sign-off.