TITLE:
Calibration of Nondestructive Assay Instruments: An Application of Linear Regression and Propagation of Variance
AUTHORS:
Stephen Croft, Tom Burr
KEYWORDS:
Linear Calibration; Estimation Errors in Weights for Weighted Least Squares; Non-Destructive Assay; Variance Propagation
JOURNAL NAME:
Applied Mathematics,
Vol.5 No.5,
March
24,
2014
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.