Impact of Bias-Correction on Measurement Uncertainties in the Statistical Evaluation of Material Balances

Nuclear material is repeatedly measured as it moves within and between material balance areas (MBA’s). Since different measurement instruments or methods might be used on the same materials at different measurement points, relatively small measurement biases can have considerable impact on material balances, in particular, for MBA’s that process significant material amounts. Such MBA’s might realize statistically significant inventory differences (ID’s), or unacceptably large ID uncertainties, as a result of accumulated differences due to minor biases between measurement methods. Bias-correction can be used to reduce such measurement biases. How this bias-correction affects the uncertainties of the measurement process should be understood and incorporated into the evaluation of the statistical significance of ID’s. In this work, the impact of bias-correction on measurement uncertainty is discussed for several types of measurement error models. Of primary interest, a relatively complex case is considered where a more capable, more expensive measurement method is used to estimate the bias of a less expensive, less capable method. This situation can arise when the more capable method is simply too expensive in terms of cost or time for routine use while the less capable method, when used in conjunction with the superior method, is sufficient to meet accuracy and precision requirements. In addition, the lack of applicable measurement standards for the inferior method necessitates the use of measurements of actual process material for establishing instrument performance. In this latter application, several initial measurements of the same process materials are made with both the more capable and less capable methods. The estimated bias between the methods is then used to bias-correct subsequent process material measurements made using the less capable method. The measurement uncertainties associated with both measurement methods are then incorporated into the uncertainty associated with the bias-corrected result.