Efficient Pooling Designs and Screening Performance in Group Testing for Two Types of Defectives

Group testing is utilized in the case when we want to find a few defectives among a large amount of items. Testing
$n$
items one by one requires
$n$
tests, but if the ratio of defectives is small, group testing is an efficient way to reduce the number of tests. Many researches have been developed for group testing for a single type of defectives. In this paper, we consider the case where two types of defective A and B exist. For two types of defectives, we develop a belief propagation algorithm to compute the marginal posterior probability of defectives. Furthermore, we construct several kinds of collections of pools in order to test for A and B. And, by utilizing our belief propagation algorithm, we evaluate the performance of group testing by conducting simulations.