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RESEARCH PAPERS

Reliability of Sampling Inspection Schemes Applied to Replacement Steam Generators

[+] Author and Article Information
Guy Roussel

 Association Vinçotte Nuclear, Rue Walcourt 148 Walcourtstraat, B-1070 Brussels, Belgiumgr@avn.be

Leon Cizelj

 Institut “Jožef Stefan,” Jamova 39, SI-1000 Ljubljana, SloveniaLeon.Cizelj@ijs.si

J. Pressure Vessel Technol 129(1), 109-117 (Mar 21, 2006) (9 pages) doi:10.1115/1.2389027 History: Received July 14, 2005; Revised March 21, 2006

The basis for determining the size of the random sample of tubes to be inspected in replacement steam generators is revisited in this paper. A procedure to estimate the maximum number of defective tubes left in the steam generator after no defective tubes have been detected in the randomly selected inspection sample is proposed. A Bayesian estimation is used to obtain closed-form solutions for uniform, triangular, and binomial prior densities describing the number of failed tubes in steam generators. It is shown that the particular way of selecting the random inspection sample (e.g., one sample from both SG, one sample from each SG, etc.) does not affect the results of the inspection and also the information obtained about the state of the uninspected tubing, as long as the inspected steam generators belong to the same population. Numerical examples further demonstrate two possible states of the knowledge existing before the inspection of the tubing. First, virtually no knowledge about the state of the steam generator tubing before the inspection is modeled using uniform and triangular prior densities. It is shown that the knowledge about the uninspected part of the tubing strongly depends on the size of the sample inspected. Further, even small inspection samples may significantly improve our knowledge about the uninspected part. On the other hand, rather strong belief on the state of the tubing prior to the inspection is modeled using binomial prior density. In this case, the knowledge about the uninspected part of the tubing is virtually independent on the size of the sample. Furthermore, it is shown qualitatively and quantitatively that such inspection brings no additional knowledge on the uninspected part of the tubing.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 2

Expected number of undetected defective tubes with uniform prior and 0 defects found in the sample

Grahic Jump Location
Figure 3

Posteriors with different sample sizes with binomial prior (p=0.004) and 0 defects found in the sample

Grahic Jump Location
Figure 4

Expected number of undetected defective tubes with binomial prior (p=0.004) and 0 defects found in the sample

Grahic Jump Location
Figure 1

Posteriors with different sample sizes with uniform prior and 0 defects found in the sample

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