It is instructive to show how the points on this curve are obtained, once we have a sampling plan (n,c) - later we will demonstrate how a sampling plan (n,c) is obtained.
We assume that the lot size N is very large, as compared to the sample size n, so that removing the sample doesn't significantly change the remainder of the lot, no matter how many defects are in the sample. Then the distribution of the number of defectives, d, in a random sample of n items is approximately binomial with parameters n and p, where p is the fraction of defectives per lot.
The probability of observing exactly d defectives is given by