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Bayesian Analysis of the Sequential Inspection Plan via the Gibbs Sampler

Author

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  • Young H. Chun

    (Department of Information Systems and Decision Sciences, E. J. Ourso College of Business, Louisiana State University, Baton Rouge, Louisiana 70803)

Abstract

A complex product, such as a software system, is often inspected more than once in a sequential manner to further improve its quality and reliability. In such a case, a particularly important task is to accurately estimate the number of errors still remaining in the product after a series of multiple inspections. In the paper, we first develop a maximum likelihood method of estimating both the number of undiscovered errors in the product and the detection probability. We then compare its performance with that of an existing estimation method that has several limitations. We also propose a Bayesian method with noninformative priors, which performs very well in a Monte Carlo simulation study. As the prior knowledge is elicited and incorporated in the analysis, the prediction accuracy of the Bayesian method improves even further. Thus, it would be worthwhile to use various estimation methods and compare their estimates in a specific inspection environment.

Suggested Citation

  • Young H. Chun, 2008. "Bayesian Analysis of the Sequential Inspection Plan via the Gibbs Sampler," Operations Research, INFORMS, vol. 56(1), pages 235-246, February.
    • Handle: RePEc:inm:oropre:v:56:y:2008:i:1:p:235-246
    DOI: 10.1287/opre.1070.0501
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    References listed on IDEAS

    as
    1. Douglas G. Bonett & J. Arthur Woodward, 1994. "Sequential Defect Removal Sampling," Management Science, INFORMS, vol. 40(7), pages 898-902, July.
    2. Raz, Tzvi & Bricker, Dennis, 1993. "Sequencing of inspection operations subject to errors," European Journal of Operational Research, Elsevier, vol. 68(2), pages 251-264, July.
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    Cited by:

    1. Barry Anderson & Emanuele Borgonovo & Marzio Galeotti & Roberto Roson, 2014. "Uncertainty in Climate Change Modeling: Can Global Sensitivity Analysis Be of Help?," Risk Analysis, John Wiley & Sons, vol. 34(2), pages 271-293, February.
    2. Chun, Young H., 2012. "Monte Carlo analysis of estimation methods for the prediction of customer response patterns in direct marketing," European Journal of Operational Research, Elsevier, vol. 217(3), pages 673-678.
    3. Borgonovo, E., 2010. "The reliability importance of components and prime implicants in coherent and non-coherent systems including total-order interactions," European Journal of Operational Research, Elsevier, vol. 204(3), pages 485-495, August.
    4. Chun, Young H., 2016. "Designing repetitive screening procedures with imperfect inspections: An empirical Bayes approach," European Journal of Operational Research, Elsevier, vol. 253(3), pages 639-647.

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