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Finding a Single Defective in Binomial Group-Testing

Satindar Kumar and Milton Sobel
Journal of the American Statistical Association
Vol. 66, No. 336 (Dec., 1971), pp. 824-828
DOI: 10.2307/2284234
Stable URL: http://www.jstor.org/stable/2284234
Page Count: 5
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Finding a Single Defective in Binomial Group-Testing
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Abstract

The problem of finding a single defective item from an infinite binomial population is considered when group-testing is possible, i.e., when we can test any number of units x simultaneously and find out in one test if all x are good or if at least one of the x is defective. An optimal procedure is obtained in the sense that it minimizes the expected number of tests required to find one defective. Upper and lower bounds are derived using information theory and the relation of our procedure to the Huffman algorithm and the corresponding cost is studied.

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