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Group testing is the problem of identifying up to d defectives in a set of n elements by testing subsets for the presence of defectives. Let t(n, d, s) be the optimal number of tests needed by an s-stage strategy in the strict group testing model where the searcher must also verify that no more than d defectives are present. We develop combinatorial tools that are powerful enough to compute man...

Tool wear is a frequent and natural part in many machining processes and is a systematic assignable cause. The fraction of defectives would rise as the tool deteriorates. When the fraction defective reaches a certain level, the tool must be replaced. To minimize the defective parts and the overall tool costs, the optimal tool replacement time needs to be determined. Process capability indices (...

This extended abstract provides an overview of the results presented in [8, 9] regarding the large-coalition asymptotics of collusion-resistant fingerprinting and the asymptotics of group testing for large numbers of defectives.

Group testing is the problem to identify up to d defectives out of n elements, by testing subsets for the presence of defectives. Let t(n, d, s) be the optimal number of tests needed by an s-stage strategy in the strict group testing model where the searcher must also verify that at most d defectives are present. We start building a combinatorial theory of strict group testing. We compute many ...