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Calibration of Nondestructive Assay Instruments: An Application of Linear Regression and Propagation of Variance

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DOI: 10.4236/am.2014.55075    5,378 Downloads   6,589 Views   Citations

ABSTRACT

Several nondestructive assay (NDA) methods to quantify special nuclear materials use calibration curves that are linear in the predictor, either directly or as an intermediate step. The linear response model is also often used to illustrate the fundamentals of calibration, and is the usual detector behavior assumed when evaluating detection limits. It is therefore important for the NDA community to have a common understanding of how to implement a linear calibration according to the common method of least squares and how to assess uncertainty in inferred nuclear quantities during the prediction stage following calibration. Therefore, this paper illustrates regression, residual diagnostics, effect of estimation errors in estimated variances used for weighted least squares, and variance propagation in a form suitable for implementation. Before the calibration can be used, a transformation of axes is required; this step, along with variance propagation is not currently explained in available NDA standard guidelines. The role of systematic and random uncertainty is illustrated and expands on that given previously for the chosen practical NDA example. A listing of open-source software is provided in the Appendix.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Croft, S. and Burr, T. (2014) Calibration of Nondestructive Assay Instruments: An Application of Linear Regression and Propagation of Variance. Applied Mathematics, 5, 785-798. doi: 10.4236/am.2014.55075.

References

[1] Chatterjee, S. (2013) Handbook of Regression Analysis. Wiley Handbooks in Applied Statistics, Hoboken.
[2] Reilly, D., Ensslin, N., Smith Jr., H. and Kreiner, S., Eds. (1991) Passive Nondestructive Assay of Nuclear Materials. US Nuclear Regulatory Commission Report NUREG/CR-5500.
[3] Topping, J. (1957) Errors of Observation and Their treatment (Revised Edition). The Institute of Physics, Chapman and Hall Limited, London.
[4] Bevington, P. and Robinson, D. (2002) Data Reduction and Error Analysis for the Physical Sciences. McGraw Hill, New York.
[5] Jaech, J. (1980) Statistical Analysis for Assay Systems. In: Sher, R. and Untermyer II, S., Eds., The Detection of Fissionable Materials by Nondestructive Means, American Nuclear Society, La Grange Park.
[6] Keepin, G. (1980) Nuclear Safeguards—A Global Issue. Los Alamos Science, 68-87.
[7] Krutchkoff, R. (1967) Classical and Inverse Regression Methods of Calibration. Technometrics, 9, 425-439.
http://dx.doi.org/10.1080/00401706.1967.10490486
[8] Willink, R. (2008) Estimation and Uncertainty in Fitting Straight lines to Data: Different Techniques. Metrologia, 45, 290-298. http://dx.doi.org/10.1088/0026-1394/45/3/005
[9] Burr, T., Pickrell, M., Rinard, P. and Wenz, T. (1999) Data Mining: Applications to Nondestructive Assay Data. Journal of Nuclear Materials Management, 27, 40-47.
[10] Burr, T., Dowell, J., Trellue, H. and Tobin, S. (2014) Measuring the Effects of Data Mining on Inference. Encylopedia of Information Sciences, 3rd Edition.
[11] Burr, T., Croft, S. and Reed, C. (2012) Least-Squares Fitting with Errors in the Response and Predictor. International Journal of Metrology and Quality Engineering, 3, 117-123.
http://dx.doi.org/10.1051/ijmqe/2012010
[12] Team, R. (2010) A Language and Environment for Statistical Computing, Vienna, Austria, R Foundation for Statistical Computing. www.R-project.org
[13] Burr, T. and Hamada, M.S. (2013) Revisiting Statistical Aspects of Nuclear Material Accounting Science and Technology of Nuclear Installations. 2013, 961360. http://dx.doi.org/10.1155/2013/961360
[14] Burr, T., Kawano, T., Talou, P., Pen, F., Hengartner, N. and Graves, T. (2011) Alternatives to the Generalized Least Squares Solution to Peele’s Pertinent Puzzle. Algorithms, 4, 115-130. http://dx.doi.org/10.3390/a4020115
[15] Carroll, R., Wu, J. and Ruppert, D. (1988) The Effect of Weights in Weighted Least Squares Regression. Journal of the American Statistical Association, 83, 1045-1054.
http://dx.doi.org/10.1080/01621459.1988.10478699
[16] Carroll, R. and Cline, D. (1988) An Asumptotic Theory for Weighted Least Squares with Weights Estimated by Replication. Biometrika, 75, 35-41. http://dx.doi.org/10.1093/biomet/75.1.35
[17] Liu, W., Lin, S. and Piegorsch, W. (2008) Construction of Exact Simultaneous Confidence Bands for a Simple Linear Regression Model. International Statistical Review, 76, 39-57.
[18] Croft, S., Burr, T. and Favalli, A. (2012) A Simple-Minded Direct Approach to Estimating the Calibration Parameter for Proportionate Data. Radiation Measurements, 47, 486-491.
http://dx.doi.org/10.1016/j.radmeas.2012.04.015
[19] Henry, M., Croft, S., Zhu, H. and Villani, M. (2007) Representing Full-Energy Peak Gamma-Ray Efficiency Surfaces in Energy and Density When the Calibration Data Is Correlated. Waste Management Symposia, 25 February-1 March 2007, Tucson, 7325.

  
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