Article Article
Joint Estimation of NDE Inspection Capability and Flaw-Size Distribution for In-Service Aircraft Inspections

Nondestructive evaluation (NDE) is widely used in the aerospace industry, using scheduled maintenance inspections to detect cracks or other anomalies in structural and rotating components. Life prediction and inspection interval decisions in aerospace applications require knowledge of the size distribution of unknown existing cracks and the probability of detecting (POD) a crack, as a function of crack characteristics (e.g., crack length). The POD for a particular inspection method is usually estimated through laboratory experiments on a given specimen set. These experiments, however, cannot duplicate the conditions of in-service inspections. Quantifying the size distribution of unknown existing cracks is more difficult. If NDE signal strength is recorded at all inspections and if crack-length information is obtained after ‘‘crack find’’ inspections, it is possible to estimate the joint distribution of crack length, noise response, and signal response. This joint distribution can then be used to estimate both the in-service POD and the crack-length distribution at a given period of service time. In this article, we present a statistical model to describe the data and illustrate a Bayesian method to do the estimation and quantify uncertainty.


1. MIL-HDBK-1823A. Nondestructive Evaluation System Reliability Assessment. Standardization Order Desk, Philadelphia, PA (2009).

2. M. Li, W. Q. Meeker, and R. B. Thompson. Review of Progress in Quantitative Nondestructive Evaluation 30:1541–1548 (2011).

3. M. Li and W. Q. Meeker. Review of Progress in Quantitative Nondestructive Evaluation 28:1769–1776 (2009).

4. D. B. Olin and W. Q. Meeker. Technometrics 38:95–112 (1996).

5. F. W. Spencer. Technometrics 38:122–124 (1996).

6. C Annis. R package: mh1823, Version, Last accessed March 2010 (2009).

7. P. Hovey, W. Q. Meeker, and M. Li. Review of Progress in Quantitative Nondestructive Evaluation 28:1832–1839 (2009).

8. M. Davidian and D. M. Giltinan. Nonlinear Models for Repeated Measurement Data. Chapman Hall, London (1995).

9. R. A. Johnson and D. W. Wichern. Applied Multivariate Statistical Analysis (5th Edition). Prentice Hall, New Jersey (2001).

10. M. Li, N. Nakagawa, B. F. Larson, and W. Q. Meeker. (2011). Preprint available at: http://www.stat.–05.pdf (last accessed January, 2012).

11. Y. Pawitan. In All Likelihood: Statistical Modelling and Inference Using Likelihood. Oxford University Press, New York (2001).

12. W. Q. Meeker and L. A. Escobar. Statistical Methods for Reliability Data. Wiley, New York (1998).

13. OpenBUGS, Version 3.2.1. Available at: accessed May 2011.

14. D. J. Lunn, A. Thomas, N. Best, and D. Spiegelhalter. Statistics and Computing 10:325–337 (2000).

15. A. Gelman, J. B. Carlin, H. S. Stern, and D. B. Rubin. Bayesian Data Analysis (Second Edition). Chapman and Hall, Boca Raton, Florida (2003).

16. Y. Wang and W. Q. Meeker. Review of Progress in Quantitative Nondestructive Evaluation 25:1870–1877 (2006).

Usage Shares
Total Views
34 Page Views
Total Shares
0 Tweets
0 PDF Downloads
0 Facebook Shares
Total Usage