| Abstract [eng] |
In the Thesis, the author investigated four Binomial Group Testing (BGT) procedures: Modified Dorfman (MD), Sterrett (St), Square Array (A2), and Pairwise Testing (PT). The optimal configurations were previously derived in the literature numerically for MD and ST. For A2, only lower and upper bounds were known. In this work, the conjectures regarding MD and ST were justified analytically. For A2, an unknown analytical expression was discovered. In the case of PT, another problem was solved: the author derived the exact form of the moment-generating function for the total number of tests (TNT). Using the latter three limit theorems were proved for TNT: the Central Limit Theorem, the Law of Large Numbers, and the Large Deviation Principle. Finally, the problem of finding the Optimal Cut-Point (OCP) in the general BGT context was tackled, and the algorithm for finding the approximate OCP was proposed. There were a lot of examples given, and the limits of applicability of the results obtained were discussed. |
