Group Testing in the Presence of Test Error; An Extension of the Dorfman Procedure

A group test is a test performed on a group of more than one item in which a good reading indicates the group contains no defective items and a defective reading indicates the presence of at least one defective. A simple procedure, proposed by Dorfman, for classifying the members of an infinite population into defective and non-defective items, is to test, groups of size k, classify the entire group as non-defective if the group test reads good, and otherwise test and classify each of the k items individually. Dorfman has given the group size k, depending on the known population fraction defective, which maximizes the expected number of items classified per test. We consider an extension of Dorfman's procedure applicable to the case in which there is a known probability of a test outcome not corresponding to the true state of the group or item under test.