Probability of detection (POD) is commonly used to measure a nondestructive evaluation (NDE) inspection procedure’s performance. Due to inherent variability in the inspection procedure caused by variability in factors such as crack morphology and operators, it is important, for some purposes, to model POD as a random function. Traditionally, inspection variabilities are pooled and an estimate of the mean POD (averaged over all sources of variability) is reported. In some applications it is important to know how poor typical inspections might be, and this question is answered by estimating a quantile of the POD distribution. This article shows how to fit and compare different models to repeated-measures hit–miss data with multiple inspections with different operators for each crack and shows how to estimate the mean POD as well as quantiles of the POD distribution for binary (hit–miss) NDE data. We also show how to compute credible intervals (quantifying uncertainty due to limited data) for these quantities using a Bayesian estimation approach. We use NDE for the detection of fatigue cracks as the motivating example, but the concepts apply more generally to other NDE applications areas.
1. MIL-HDBK-1823A, Nondestructive evaluation system reliability assessment, 2009. http://www.statisticalengineering.com/mh1823/MIL-HDBK-1823A(2009).pdf (accessed Feb. 5, 2017).
2. M. Li, W. Q. Meeker, and F. W. Spencer, Rev. Prog. Quantitative Nondestructive Eval. 31, 1725–1732 (2012). D. O. Thompson and D. E. Chimenti (Eds) (American Institute of Physics, New York).
3. M. Li, W. Q. Meeker, and R. B. Thompson, Technometrics. 56, 78–91 (2014). DOI: 10.1080/00401706.2013.818580.
4. M. Li, F. W. Spencer, and W. Q. Meeker, Mater Eval. 73, 89–95 (2015).
5. W. H. Lewis, et al., USAF SA-ALC/MEE 76-6-38-1, 1978. http://www.dtic.mil/cgi-bin/GetTRDoc?Location=U2doc=GetTRDoc.pdf AD=ADA072097 (accessed Feb. 5, 2017).
6. A. P. Berens and P. W. Hovey, USAF Report No. AFWAL-TR-81-4160, 1981. http://www.dtic.mil/cgi-bin/GetTRDoc?AD=ADA114467 (accessed Feb. 5, 2017).
7. R. Singh, Report No. Karta-3510-99-01, 2000. https://www.cnde.iastate.edu/mapod/Reference%20Documents/Karta%20pod%201970-1999.pdf (accessed Feb. 5, 2017).
8. R. Peto, Appl Stat. 22, 86–91 (1973). DOI: 10.2307/2346307.
9. B. W. Turnbull, J Royal Stat Soc. 38, 290–295 (1976).
10. W. Q. Meeker and L. A. Escobar, Statistical Methods for Reliability Data (John Wiley & Sons, 1998).
11. B. P. Carlin and T. A. Louis, Bayesian Methods for Data Analysis, 3rd ed. (Chapman & Hall, New York, 2008).
12. A. Gelman, et al., Bayesian Data Analysis, 2nd ed. (Chapman & Hall, New York, 2004).
13. W. R. Gilks, S. Richardson, and D. Spiegelhalter, Markov Chain Monte Carlo in Practice (Chapman and Hall, New York, 1996).
14. J. M. Bernardo and A. F. M. Smith, Bayesian Theory (Wiley, Chichester, 2000).
15. OpenBUGS, 2015. http://www.openbugs.net/w/Downloads (accessed Feb. 5, 2017).
16. A. Gelman, Bayesian Anal. 1, 515–534 (2006). DOI: 10.1214/06-BA117A.
17. A. E. Gelfand, S. K. Sahu, and B. P. Carlin, Biometrika. 82, 479–488 (1995). DOI: 10.1093/biomet/82.3.479.
18. W. J. Browne, et al., J. Royal Stat Soc. 172, 579–598 (2009). DOI: 10.1111/j.1467-985X.2009.00586.x.
19. J. Liu, D. J. Nordman, and W. Q. Meeker, Am Stat. 70, 275–284 (2016). DOI: 10.1080/00031305.2016.1158738.
20. R. E. Kass and A. E. Raftery, J Am Stat Assoc. 90, 773–795 (1995). DOI: 10.1080/01621459.1995.10476572.
28 Page Views
0 PDF Downloads
0 Facebook Shares