Lot Acceptance OC Curve Calculator for Medical Device Inspection
An operating characteristic curve shows how well a sampling plan separates good lots from bad ones. This calculator gives the chance of accepting a lot at any defect rate for plans with an acceptance number of zero, one or two, and estimates the average outgoing quality.
Your numbers
Your results
Poisson approximation, accurate when the sample is small relative to the lot and the defect rate is low. Use exact hypergeometric or binomial values for small lots or high defect rates.
Probability of acceptance vs lot defect rate
Sweeps True lot defect rate from 0 to 10, holding your other inputs fixed.
Apply sampling plans in your ERP
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How to use it
Enter your sample size, choose the acceptance number and set the assumed true defect rate of the lot. The tool reports the probability of acceptance and rejection and the average outgoing quality. The chart plots the full curve across defect rates from 0 to 10%, which is how you see the consumer's risk at a defect rate you cannot tolerate and the producer's risk at a rate you consider good.
The math
With a defect rate p and sample size n, the number of defects in the sample is approximately Poisson with mean np. For acceptance number zero, the probability of acceptance is e to the minus np. For one it adds np, and for two it adds np squared over two, all multiplied by e to the minus np. AOQ approximates p times Pa times the unsampled fraction of the lot.
- c = 0: Pa = exp(-np)
- c = 1: Pa = exp(-np) x (1 + np)
- c = 2: Pa = exp(-np) x (1 + np + np^2 / 2)
- AOQ = p x Pa x (1 - n / N)
Common mistakes
A plan with c equal to zero feels strict but can still accept bad lots when the sample is small. At a 1% defect rate, a sample of 80 accepts about 45% of the time. Many teams expect sampling to guarantee a defect-free lot, but it only controls risk. Critical characteristics should rely on process validation and 100% inspection or verified automation, not on sampling alone.
Frequently Asked Questions
What is the consumer's risk?
It is the probability of accepting a lot whose quality is at or worse than an unacceptable level. On the OC curve, it is the acceptance probability at that defect rate. Lower it by increasing sample size or lowering the acceptance number.
Why does c = 0 have such a steep curve?
With zero acceptance, any single defect rejects the lot, so acceptance falls quickly as the defect rate rises. The curve still has a tail, so poor lots can pass when the sample is small.
How does this relate to AQL tables?
AQL tables, such as the ANSI/ASQ Z1.4 family, are pre-built plans with defined OC curves. This tool lets you see the curve of any n and c, including custom plans such as those from validation protocols.
When should I use hypergeometric instead?
When the sample is more than about ten percent of the lot, or the lot is small. The Poisson shortcut overstates the chance of finding a defect in those cases, so use an exact calculation.
If your inspection plans and lot disposition live in the ERP, we can help review how to calculate risk and apply the right plan by item and supplier.
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