Single-Sampling Plans for Attributes
15.2.1 Definition of a Single-Sampling Plan
Suppose that a lot of size N has been submitted for inspection. A single-sampling plan is
defined by the sample size n and the acceptance number c. Thus, if the lot size is N = 10,000,then the sampling plan
n = 89
c = 2
means that from a lot of size 10,000 a random sample of n = 89 units is inspected and the
number of nonconforming or defective items d observed. If the number of observed defectives
d is less than or equal to c = 2, the lot will be accepted. If the number of observed defectives
d is greater than 2, the lot will be rejected. Since the quality characteristic inspected is
an attribute, each unit in the sample is judged to be either conforming or nonconforming. One
or several attributes can be inspected in the same sample; generally, a unit that is nonconforming
to specifications on one or more attributes is said to be a defective unit. This procedure
is called a single-sampling plan because the lot is sentenced based on the information
contained in one sample of size n.
15.2.2 The operating characteristic Curve
An important measure of the performance of an acceptance-sampling plan is the operatingcharacteristic
(OC) curve. This curve plots the probability of accepting the lot versus the lot
fraction defective. Thus, the OC curve displays the discriminatory power of the sampling
plan. That is, it shows the probability that a lot submitted with a certain fraction defective will
be either accepted or rejected. The OC curve of the sampling plan n = 89, c = 2 is shown in