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Sterrett Procedure for the Generalized Group Testing Problem

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  • Yaakov Malinovsky

    (University of Maryland)

Abstract

Group testing is a useful method that has broad applications in medicine, engineering, and even in airport security control. Consider a finite population of N items, where item i has a probability pi to be defective. The goal is to identify all items by means of group testing. This is the generalized group testing problem. The optimum procedure, with respect to the expected total number of tests, is unknown even in case when all pi are equal. (Hwang 1975) proved that an ordered partition (with respect to pi) is the optimal for the Dorfman procedure (procedure D), and obtained an optimum solution (i.e., found an optimal partition) by dynamic programming. In this paper, we investigate the Sterrett procedure (procedure S). We provide close form expression for the expected total number of tests, which allows us to find the optimum arrangement of the items in the particular group. We also show that an ordered partition is not optimal for the procedure S or even for a slightly modified Dorfman procedure (procedure D′). This discovery implies that finding an optimal procedure S appears to be a hard computational problem. However, by using an optimal ordered partition for all procedures, we show that procedure D′ is uniformly better than procedure D, and based on numerical comparisons, procedure S is uniformly and significantly better than procedures D and D′.

Suggested Citation

  • Yaakov Malinovsky, 2019. "Sterrett Procedure for the Generalized Group Testing Problem," Methodology and Computing in Applied Probability, Springer, vol. 21(3), pages 829-840, September.
    • Handle: RePEc:spr:metcap:v:21:y:2019:i:3:d:10.1007_s11009-017-9601-4
    DOI: 10.1007/s11009-017-9601-4
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    References listed on IDEAS

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    1. Shaul K. Bar-Lev & Onno Boxma & Wolfgang Stadje & Frank A. Duyn Schouten, 2010. "A Two-Stage Group Testing Model for Infections with Window Periods," Methodology and Computing in Applied Probability, Springer, vol. 12(3), pages 309-322, September.
    2. Bilder, Christopher R. & Tebbs, Joshua M. & Chen, Peng, 2010. "Informative Retesting," Journal of the American Statistical Association, American Statistical Association, vol. 105(491), pages 942-955.
    3. A. K. Chakravarty & J. B. Orlin & U. G. Rothblum, 1982. "Technical Note—A Partitioning Problem with Additive Objective with an Application to Optimal Inventory Groupings for Joint Replenishment," Operations Research, INFORMS, vol. 30(5), pages 1018-1022, October.
    4. Lei Zhu & Jacqueline M. Hughes-Oliver & S. Stanley Young, 2001. "Statistical Decoding of Potent Pools Based on Chemical Structure," Biometrics, The International Biometric Society, vol. 57(3), pages 922-930, September.
    5. Chakravarty, Amiya K., 1982. "Inventory grouping for joint replenishment," Engineering Costs and Production Economics, Elsevier, vol. 7(1), pages 19-24, July.
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    Cited by:

    1. Daniel K. Sewell, 2022. "Leveraging network structure to improve pooled testing efficiency," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(5), pages 1648-1662, November.

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