Functions

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.