Fig. 15.2. It is easy to demonstrate how the points on this curve are obtained. Suppose that
the lot size N is large (theoretically infinite). Under this condition, the distribution of the number
of defectives d in a random sample of n items is binomial with parameters n and p, where
p is the fraction of defective items in the lot. An equivalent way to conceptualize this is to
draw lots of N items at random from a theoretically infinite process, and then to draw random
samples of n from these lots. Sampling from the lot in this manner is the equivalent of sampling
directly from the process. The probability of observing exactly d defectives is
(15.1)
The probability of acceptance is simply the probability that d is less than or equal to c, or