Supplier Lot Acceptance Probability Calculator (OC Curve)
A sampling plan is a bet. This calculator shows the odds: for a given supplier defect rate, how often does a lot pass your plan, and how many bad parts get through? It plots the operating characteristic, or OC, curve so you can compare plans before you set them in the ERP inspection plan.
Your numbers
Units inspected from each lot.
Lot is accepted if defects found are at or below this number.
Actual percent nonconforming in the lot or process.
Your results
Uses the binomial model, appropriate when the lot is much larger than the sample. For small lots use the hypergeometric model.
Probability of acceptance vs true defect rate
Sweeps True supplier defect rate from 0 to 15, holding your other inputs fixed.
Review incoming inspection plans
Optional: an expert look at how inspection plans and supplier results are configured in your ERP.
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How to use it
Enter the sample size and acceptance number from your inspection plan. Set the true defect rate to the level you are worried about, such as the supplier's historic rate or your acceptable quality limit. Read the probability of acceptance, then move the defect rate to see how the plan reacts. A good plan accepts almost all lots at the quality you want and rejects almost all lots at the quality you fear.
- Use sample size from your inspection plan or standard
- Test the rate you consider acceptable, then the rate you consider bad
- Compare c=0 and c=1 at the same sample size
- Look at the chart, not one point
The math
For a lot that is much larger than the sample, the number of defects found follows a binomial distribution. The probability of acceptance with c equal to zero is (1 minus p) to the power n. With c equal to one it adds n times p times (1 minus p) to the power n minus one, and so on. Average outgoing quality, for large lots and with rejected lots replaced by good lots, is the defect rate times the probability of acceptance.
Reading the OC curve
At the default plan of 80 samples and accept on one, a 2 percent defective lot passes roughly half the time. That surprises many people: sampling does not catch most defects in a lot at modest defect rates. If that risk is too high, increase the sample size or tighten the acceptance number, and shift focus to supplier process control, since inspection alone cannot make quality. Expected rejected lots per year helps estimate workload.
Common mistakes
Confusing the acceptance probability with the share of defects found is common. Another error is applying the binomial model to a lot of 100 units with a sample of 50, where the hypergeometric model is more accurate. Also, a lot that passes is not proof of a good lot, so keep supplier data, process audits and corrective action alongside incoming inspection. Record the chosen plan and its risk in the supplier quality agreement.
Frequently Asked Questions
What is an OC curve?
An operating characteristic curve plots the probability that a lot is accepted against the true defect rate of the lot. It shows the real protection a sampling plan gives, including the chance of accepting bad lots and rejecting good ones.
Is this the same as AQL?
No. AQL is a quality level that a plan should usually accept. This calculator works for any plan and any defect rate, so you can see what a plan does at AQL, at the limiting quality, and anywhere between.
Why does c=0 sampling reject more lots?
With zero acceptance, one defect in the sample rejects the lot. That is stricter at low defect rates, but it also makes the plan less forgiving of random variation, so good suppliers can see more rejects.
When should I not use this?
Do not use it for small lots where the sample is more than about 10 percent of the lot, or for variable sampling plans. Use the hypergeometric distribution or the plan's published tables in those cases.
If you want sampling plans, results and supplier history visible together in your ERP, Netray can help build that view on your own data.
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