FINITE AND INFINITE MODELS FOR GENERALIZED GROUP-TESTING WITH UNEQUAL PROBABILITIES OF SUCCESS FOR EACH ITEM

Abstract

In group testing, any number of units from the same or different sources can be tested, but each test of a batch of, say, x units gives one of two possible results: (1) either all x units are good or (2) at least one of the x units is defective and one does not know which one. This chapter presents a classification of units efficiently in the sense of minimizing the number of tests required. Each value of i corresponds to a different source or stream of units, and each stream represents an assembly line type of operation with an unending number of units coming forth to be tested. Each unit from the ith stream can only be good or defective. All units from the same or different streams represent independent binomial chance variables. The one restriction that is put on the plan or strategy for testing units is that no stream should be held up indefinitely, that is, any unit in any of the k streams is classified in some finite number of tests. For any set of qi-values, one can always write these as powers of one q.