Group-Sequential Leak-Testing of Sealed Radium Sources

Pasternack, Bernard S.; Böhning, Dorith; Thomas, James B.

doi:10.2307/1267917

Cited by 5 publications

(2 citation statements)

References 21 publications

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“…is given by (a)), but did not explicitly examine the numerical value of this uncertainty or its implications; this was done subsequently by Thomas et al (1975) and Pasternack et al (1976).…”

Section: Number Of Tests Formentioning

confidence: 99%

Group-testing, halving procedures, and binary search^∗

Pasternack

Sobel

Thomas

1987

Communications in Statistics - Theory and Methods

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Section: Number Of Tests Formentioning

confidence: 99%

Group-testing, halving procedures, and binary search^∗

Pasternack

Sobel

Thomas

1987

Communications in Statistics - Theory and Methods

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“…In some contexts, the positive groups may even represent a risk for the safety of the persons that perform the tests. An example of such applications are leak testing procedures aimed at guaranteeing the safety of sealed radioactive sources [31,32]. Radioactive sources are widely used in medical, industrial and agricultural applications, as well as in scientific research.…”

Section: Introductionmentioning

confidence: 99%

Constraining the number of positive responses in adaptive, non-adaptive, and two-stage group testing

Bonis

2015

J Comb Optim

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Group testing is a well known search problem that consists in detecting the defective members of a set of objects O by performing tests on properly chosen subsets (pools) of the given set O. In classical group testing the goal is to find all defectives by using as few tests as possible. We consider a variant of classical group testing in which one is concerned not only with minimizing the total number of tests but aims also at reducing the number of tests involving defective elements. The rationale behind this search model is that in many practical applications the devices used for the tests are subject to deterioration due to exposure to or interaction with the defective elements. In this paper we consider adaptive, non-adaptive and two-stage group testing. For all three considered scenarios, we derive upper and lower bounds on the number of "yes" responses that must be admitted by any strategy performing at most a certain number t of tests. In particular, for the adaptive case we provide an algorithm that uses a number of "yes" responses that exceeds the given lower bound by a small constant. Interestingly, this bound can be asymptotically attained also by our twostage algorithm, which is a phenomenon analogous to the one occurring in classical group testing. For the non-adaptive scenario we give almost matching upper and lower bounds on the number of "yes" responses. In particular, we give two constructions both achieving the same asymptotic bound. An interesting feature of one of these constructions is that it is an explicit construction. The bounds for the non-adaptive and the two-stage cases follow from the bounds on the optimal sizes of new variants of d-cover free families and (p, d)-cover free families introduced in this paper, which we believe may be of interest also in other contexts.

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