Group Testing with a Dilution Effect

We study a group testing model with the presence of a dilution effect. Namely, a group containing a few defective items may possibly be mimdentified as a group containing no such items, especially when the size of the group is large. When such misidentification happens, a loss is incurred. By assuming that the dilution effect has a special form, which includes the classical model with no dilution effects as a special case, we calculate the expected cost under the Dorfman procedure and determine the optimal group size.