Year
2024
Abstract
| Many of the statistical methods used at the IAEA are based on estimates of the operator's and inspector's random and systematic error variances.For example, in sampling plan design it is assumed that the random and systematic error variances of the operator’s and the inspector’s measurements are utilized as if they were the true values of the variances. However, the true values of the variances are not known and are therefore estimates based on paired data. As estimates, they are subject to uncertainties. These uncertainties should be taken into account when designing sampling plans. Then, a confidence band around the true detection probability curve, that is based on the uncertainties of the variance estimators, would be the basis of the sampling plan design instead of the detection probability curve based on the supposed true values of the four variances. For such a confidence band, however, the distribution of the four variance estimators must be known.Another example is nuclear material accounting, where it is important to assess whether the variance estimators meet international standards. For this purpose, it is not only important to estimate the uncertainties of the four variance estimators, but also to know their distribution so that meaningful confidence intervals can be constructed. Only the confidence intervals of the estimators provide information on whether the measurement methods used in nuclear material accounting comply with international standards.This paper considers the Grubbs estimators for the estimation of the operator's and inspector's random error variance. To evaluate the accuracy of these estimators, it is necessary to know the exact distribution of the estimators. These distributions have not yet been determined analytically or experimentally by simulations. This paper presents first steps towards closing this gap. |