OC Sampling Characteristic Curve: Acceptance Probability and Risk
What Is an OC Curve?
The operating characteristic (OC) curve describes the acceptance probability Pa(p) of a sampling plan for lots with different nonconforming rates p: the smaller the p, the higher the acceptance probability, and the steeper the curve, the stronger the plan's discrimination power. The tool computes Pa exactly from the binomial distribution (or Poisson approximation) and draws the full curve and data table. The OC curve is the fundamental tool for evaluating the protective power of a sampling plan and the basis for negotiation between supplier and buyer.
How to Read the Curve
At the AQL (acceptable quality level), the acceptance probability should be 1 minus alpha (alpha is the producer's risk, usually 5%), meaning lots better than the AQL are accepted about 95% of the time. At the LTPD (lot tolerance percent defective), the acceptance probability is beta (the consumer's risk, usually 10%), meaning lots worse than the LTPD are accepted only about 10% of the time. The steeper the drop between the two points, the better the plan; the closer the curve is to an ideal step shape, the stronger the discrimination, at the cost of a larger sample size.
How to Compare and Optimize Plans
Fixing Ac and increasing n makes the curve steeper (stronger discrimination); fixing n and increasing Ac shifts the curve to the right (a looser plan). The tool supports plotting several plans simultaneously for comparison, helping you trade off sample-size cost against protection level; you can also enter target AQL and LTPD values to back-calculate a plan that satisfies the alpha and beta requirements. Comparing multiple plans makes the trade-off between sample size and protection visible and supports plan review and optimization.
How to Use It (Step by Step)
Enter the plan (n, Ac) (several can be compared), generate the OC curve and data table, mark AQL, LTPD, alpha and beta, and evaluate whether the plan meets both parties' risk requirements. Note that the OC curve assumes random sampling and a lot much larger than the sample; the curve is invalid for non-random sampling. For small lots the binomial calculation is more accurate, and the tool selects the applicable probability model automatically.