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Using a Bayesian model to jointly estimate the flaw size distribution and the pod function
Center for Nondestructive Evaluation Conference Papers, Posters and Presentations
  • M. Li, Iowa State University
  • William Q. Meeker, Iowa State University
  • P. Hovey, University of Dayton
Document Type
Conference Proceeding
Review of Progress in Quantitative Nondestructive Evaluation
Publication Date
(41.4803791, -71.5225598)

In this paper we extend previous work by the authors to jointly estimate the flaw size distribution and the POD function from simulated field inspection data. Similar to our previous work, we assume that when a crack is above a detection threshold, both the signal amplitude and the flaw size are recorded. For a signal that is above the noise floor, but below the detection threshold, only the amplitude is recorded. At all other locations we know only that the signal is below the noise floor, i.e. left censored. Now our model allows different airplanes to have different crack growth rates, and the distribution of crack growth rates is to be estimated from the data. To estimate the parameters of the model, we use a Bayesian formulation that provides a convenient structure for estimating the plane‐to‐plane differences. The Bayesian formulation also allows the use of prior information based on knowledge of physics or previous experience with similar inspection situations. For example, there may be useful information about crack growth rates and about the slope in the amplitude and crack size relationship. Use of such information can importantly improve estimation precision.


Copyright 2010 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.

This article appeared in AIP Conference Proceedings 1211 (2010): 687–694 and may be found at

Copyright Owner
American Institute of Physics
Citation Information
M. Li, William Q. Meeker and P. Hovey. "Using a Bayesian model to jointly estimate the flaw size distribution and the pod function" Kingston, RI(2009)
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