Group Testing to Eliminate Efficiently All Defectives in a Binomial Sample

A problem which has hitherto been considered only in connection with blood-testing applications1,2,3 can be shown to have industrial applications, and these have focused interest on a more general treatment of the problem. During World War I I , a great saving was accomplished in the field of blood testing by pooling a fixed number of blood samples and testing the pooled sample for some particular disease. If the disease was not present, then several people were passed by a single test; if the disease was present, then there was enough blood remaining in each blood sample to test each one separately. The amount of time, money and effort saved by such a procedure depends on how rare the disease is in the population of people being tested. In this application, the total number of people to be tested was regarded as unknown and very large. The goal of the problem treated here is the same -- namely, to separate the defective units from the good units with a minimal (or approximately minimal) number of group-tests. This problem differs from the blood-testing problem in the following respects: i. The population size N (number of people to be tested) is known at the outset.