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Journals ACM SIGMAP Bulletin Issue 18

While working at Sandia Corporation some years ago, there was a need for a mathematical model that would give the minimum number of tests that would detect the presence of certain undesirable microbes or "bugs". We assume that there exists a number of tests that will react in certain ways to the presence of individual "bugs". Unfortunately, there exist bugs for which the tests will react in exactly the same way. Therefore we must find, not just the minimum set of tests that will determine if a bug is present or not, but rather the minimum set of tests such that we can separate and detect all the bugs that are present. To illustrate the problem, assume that we have five "bugs" that could be present on a piece of equipment. Say that we have six tests that either react or do not react in some way when certain bugs are present. Further we have the problem that some tests react with certain probability to the presence of certain bugs. If we arbitrarily establish a confidence limit on this probability, and the probability falls below this level we say that the reaction is "unknown". Therefore for six tests and five bugs we could have the reaction matrix (t ij ) shown below.

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The incredible shrinking bug separation model

Woolsey, Gene
ACM SIGMAP Bulletin , Volume (18)
Association for Computing Machinery – Feb 1, 1975

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