Unbalanced Nested Random Effects Estimation of Variance Components
To investigate the contributing factors of variance in the measurement of an iodine 127 (127I) sample, we implement a nested random effects analysis of variance (ANOVA). Historically, the reported uncertainty on a measurement of 127I has been obtained by methods of forward uncertainty propagation because there is typically only one replicate of a given sample for which to estimate the uncertainty. When samples are processed there are several types of quality control (QC) standards analyzed along-side the unknown samples with two to five replicates for each. Assuming the variance observed in these replicate QC standards is representative of that of the unknown samples, we use these data in a nested random effects ANOVA to estimate the total uncertainty of a measurement. We demonstrate this approach with two sets of measurements from Idaho National Laboratory and compare the results with the forward uncertainty propagation approach. Variance component estimates for the coarsest level of the nesting structure were most imprecise because replicates were most limited at these levels. We find that the results largely agree between forward propagation and ANOVA, and the greatest contributors of variance are due to instrument variation and chemical processing, with human processing being among the smallest contributors. This analysis provides reassurance that the reported uncertainties using forward propagation are reasonable and the process is well controlled. We propose a future designed experiment to increase replicates at the coarsest level of the hierarchy to improve estimates of these variance components.