GROUP TESTING TO ELIMINATE EFFICIENTLY ALL DEFECTIVES IN A BINOMIAL SAMPLE
GROUP TESTING TO ELIMINATE EFFICIENTLY ALL DEFECTIVES IN A BINOMIAL SAMPLE
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DOI：
10.1002/j.1538-7305.1959.tb03914.x
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发表时间：
1959-01-01
影响因子：
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通讯作者：
GROLL, PA
中科院分区：
文献类型：
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作者：
SOBEL, M;GROLL, PA
在分组测试中，从总共N个单元的初始集合中取出一组x个单元，并且x个单元（1 <$x <$N）作为一个组同时进行测试，有两种可能的结果之一：所有x个单元都是好的，或者至少有一个有缺陷的单元（我们不知道有多少或哪些）。在这种类型的测试下，问题是找到第一次测试的最佳整数x，并找到选择最佳后续测试组的规则（这可能取决于已经观察到的结果），以便最小化将N个单元中的每个单元分类为良好或有缺陷所需的组测试的预期总数。它是假设N个单位可以被视为一个共同的，已知的概率P的任何一个有缺陷的独立的二项机会变量;未知的情况下，P和几个概括的问题也被认为是。
In group‐testing, a set of x units is taken from a total starting set of N units, and the x units (1 ≦ x ≦ N) are tested simultaneously as a group with one of two possible outcomes: either all x units are good or at least one defective unit is present (we don't know how many or which ones). Under this type of testing, the problem is to find the best integerxfor the first test and to find a rule for choosing the best subsequent test‐groups (which may depend on results already observed), in order to minimize the expected total number of group‐tests required to classify each of the N units as good or defective. It is assumed that the N units can be treated like independent binomial chance variables with a common, known probability p of any one being defective; the case of unknown p and several generalizations of the problem are also considered.