## Types of Sampling Plans

In single sampling, a random sample of *n* items is
selected from a lot of size *N*. If the number *d* of
nonconforming (defective) items found in the sample is
less than or equal to an acceptance number *c*, the lot is
accepted. Otherwise, the lot is rejected.
In double sampling, a sample of size *n*_{1} is drawn from the lot, and
the number *d*_{1} of nonconforming items is counted. If *d*_{1} is less
than or equal to an acceptance number *a*_{1}, the lot is accepted, and
if *d*_{1} is greater than or equal to a rejection number *r*_{1}, the lot
is rejected. Otherwise, if *a*_{1}<*d*_{1}<*r*_{1}, a second sample of size
*n*_{2} is taken, and the number of nonconforming items *d*_{2} is counted.
Then if *d*_{1}+*d*_{2} is less than or equal to an acceptance number *a*_{2},
the lot is accepted, and if *d*_{1}+*d*_{2} is greater than or equal to a
rejection number *r*_{2}=*a*_{2}+1, the lot is rejected. This notation
follows that of Schilling (1982). Note that some authors, including
Montgomery (1996), define the first rejection number using a strict
inequality.

In *Type A sampling*, the sample is intended to represent
a single, finite-sized lot, and the characteristics of the sampling
plan depend on *D*, the number of nonconforming items in the
lot, as well as *N*, *n*, and *c*.

In *Type B sampling*, the sample is intended to represent
a series of lots (or the lot size is effectively infinite), and the
characteristics of the sampling plan depend on *p*, the proportion of
nonconforming items produced by the process, as well as *n* and *c*.

A hypergeometric model is appropriate for Type A sampling, and a
binomial model is appropriate for Type B sampling.

Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.