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

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.