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A Dichotomous Search for a Geometric Random Variable

Author

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  • Refael Hassin

    (Tel-Aviv University, Tel-Aviv, Israel)

Abstract

We are given a two-state system that starts in state 0, ends in state 1, and makes a single transition from state 0 to state 1 during N periods. If the system is in state 0, it moves to state 1 in the next period with a known positive time-independent probability. Once it reaches state 1, it remains there. By observing the state of the system at some intermediate period, we can learn whether this transition occurred earlier or not. An optimal search strategy minimizes the expected number of observations needed to locate the exact transition time. In this paper we show how to compute efficiently and how to approximate the optimal strategy. Applications to the problem arise in the areas of quality control and maintenance of communication and supply lines.

Suggested Citation

  • Refael Hassin, 1984. "A Dichotomous Search for a Geometric Random Variable," Operations Research, INFORMS, vol. 32(2), pages 423-439, April.
    • Handle: RePEc:inm:oropre:v:32:y:1984:i:2:p:423-439
    DOI: 10.1287/opre.32.2.423
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    Cited by:

    1. Bendavid, Illana & Herer, Yale T., 2009. "Economic optimization of off-line inspection in a process that also produces non-conforming units when in control and conforming units when out of control," European Journal of Operational Research, Elsevier, vol. 195(1), pages 139-155, May.
    2. Hassin, Refael & Sarid, Anna, 2018. "Operations research applications of dichotomous search," European Journal of Operational Research, Elsevier, vol. 265(3), pages 795-812.
    3. Yale T. Herer & Tzvi Raz, 2000. "Optimal Parallel Inspection for Finding the First Nonconforming Unit in a Batch---An Information Theoretic Approach," Management Science, INFORMS, vol. 46(6), pages 845-857, June.
    4. Wang, Wen-Ying & Sheu, Shey-Huei & Chen, Yan-Chun & Horng, Der-Juinn, 2009. "Economic optimization of off-line inspection with rework consideration," European Journal of Operational Research, Elsevier, vol. 194(3), pages 807-813, May.
    5. Shoshana Anily & Abraham Grosfeld-Nir, 2006. "An Optimal Lot-Sizing and Offline Inspection Policy in the Case of Nonrigid Demand," Operations Research, INFORMS, vol. 54(2), pages 311-323, April.
    6. Abraham Grosfeld‐Nir & Eyal Cohen & Yigal Gerchak, 2007. "Production to order and off‐line inspection when the production process is partially observable," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(8), pages 845-858, December.
    7. S H Sheu & Y C Chen & W Y Wang & N H Shin, 2003. "Economic optimization of off-line inspection with inspection errors," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(8), pages 888-895, August.

    More about this item

    Keywords

    751 dichotomous search;

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