Functions: Types of Sampling Plans

Product	Release
SAS/QC	9.2

Functions

Types of Sampling Plans

In single sampling, a random sample of items is selected from a lot of size . If the number of nonconforming (defective) items found in the sample is less than or equal to an acceptance number , 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 of nonconforming items is counted. If is less than or equal to an acceptance number $a_{1}$ , the lot is accepted, and if is greater than or equal to a rejection number $r_{1}$ , the lot is rejected. Otherwise, if $a_1\lt d_1\lt r_1$ , a second sample of size $n_{2}$ is taken, and the number of nonconforming items $d_{2}$ is counted. Then if is less than or equal to an acceptance number $a_{2}$ , the lot is accepted, and if is greater than or equal to a rejection number , 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 , the number of nonconforming items in the lot, as well as , , and .

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 , the proportion of nonconforming items produced by the process, as well as and .

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

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SAS/QC(R) 9.2 User's Guide

Types of Sampling Plans