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Optimal Parallel Inspection for Finding the First Nonconforming Unit in a Batch---An Information Theoretic Approach

Author

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  • Yale T. Herer

    (Department of Industrial Engineering, Tel Aviv University, Ramat Aviv 69978, Israel)

  • Tzvi Raz

    (Faculty of Management, Tel Aviv University, Ramat Aviv 69978, Israel)

Abstract

We consider the case of a batch of discrete units produced by a process subject to failures under a known probability distribution function, and apply information theory to the problem of finding the first nonconforming unit in the batch at minimum cost. Two distinct but related aspects of this problem were treated: determining which units should be inspected, and determining how many units should be sent for inspection at the same time. The solution is based on the principles of inspecting the product units that maximize the reduction in the uncertainty regarding the location of the first nonconforming unit, and of minimizing the cost per unit of uncertainty reduced. These principles are formalized by means of a series of theorems leading to an easy-to-implement algorithm for managing parallel inspection. This approach is successfully compared with the optimal solution obtained with dynamic programming and with other heuristics.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:ormnsc:v:46:y:2000:i:6:p:845-857
    DOI: 10.1287/mnsc.46.6.845.11933
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    References listed on IDEAS

    as
    1. Evan L. Porteus, 1990. "Note---The Impact of Inspection Delay on Process and Inspection Lot Sizing," Management Science, INFORMS, vol. 36(8), pages 999-1007, August.
    2. Refael Hassin, 1984. "A Dichotomous Search for a Geometric Random Variable," Operations Research, INFORMS, vol. 32(2), pages 423-439, April.
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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. Liying Mu & Milind Dawande & Xianjun Geng & Vijay Mookerjee, 2016. "Milking the Quality Test: Improving the Milk Supply Chain Under Competing Collection Intermediaries," Management Science, INFORMS, vol. 62(5), pages 1259-1277, May.
    4. Muhammad Babar Ramzan & Shehreyar Mohsin Qureshi & Sonia Irshad Mari & Muhammad Saad Memon & Mandeep Mittal & Muhammad Imran & Muhammad Waqas Iqbal, 2019. "Effect of Time-Varying Factors on Optimal Combination of Quality Inspectors for Offline Inspection Station," Mathematics, MDPI, vol. 7(1), pages 1-18, January.

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    Keywords

    inspection planning; information theory;

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