sample sizes offer different levels of protection. It is illogical for the level of protection that
the consumer enjoys for a critical part or component to vary as the size of the lot varies.
Although sampling procedures such as this one were in wide use before the statistical principles
of acceptance sampling were generally known, their use has (unfortunately) not entirely
disappeared.
15.2.3 Designing a Single-Sampling Plan with a Specified OC Curve
A common approach to the design of an acceptance-sampling plan is to require that the OC
curve pass through two designated points. Note that one point is not enough to fully specify
the sampling plan; however, two points are sufficient. In general, it does not matter which two
points are specified.
Suppose that we wish to construct a sampling plan such that the probability of acceptance
is 1 − a for lots with fraction defective p1, and the probability of acceptance is b for lots
with fraction defective p2. Assuming that binomial sampling (with type-B OC curves) is
appropriate, we see that the sample size n and acceptance number c are the solution to