Purpose: To estimate the measurement uncertainty (MU) of the qualitative Anti-HBc radioimmunoassay based on the Guide to the Expression of Uncertainty in Measurement (GUM) and to redefine the gray zone near the cut-off using zeta-scores to improve the reliability of clinical decisions. Materials and Methods: The MU of the RIAKEY Anti-HBc RIA Tube assay using a Gamma 10 counter was evaluated using a bottom-up approach. Five uncertainty components were analyzed: repeatability, reproducibility, inter-detector efficiency, pipette accuracy, and inner-detector variability. Combined standard uncertainty was calculated using the root sum square method, and expanded uncertainty was estimated with a coverage factor (k=2.10) based on an approximately 95% confidence level. A zeta-score model and the cumulative distribution function (CDF) of the t-distribution were applied to establish a quantitative gray zone and calculate the probability of false classification. Results: Reproducibility was the largest contributor to MU (57.67%), followed by inter-detector efficiency (37.75%) and inner-detector variability (3.85%). The expanded uncertainty of the cut-off was calculated as 18,066 ± 412 cpm. The MU-based gray zone established using the zeta-score model reduced the indeterminate interval by approximately 67.76% compared to the conventional arbitrary criterion of cut-off ±10%. Application of the zeta-score and t-CDF allowed for the quantitative reporting of clinical results, clearly distinguishing between definitive classifications and indeterminate cases requiring retesting based on a ±2.10 zeta-score threshold. Conclusion: The MU-based gray zone optimized the decision interval and enhanced the precision of the qualitative Anti-HBc assay. The probabilistic approach utilizing zeta-scores and t-CDF provides an objective criterion for interpreting results, which is expected to strengthen the consistency and reliability of clinical decision-making in nuclear medicine in vitro diagnostics.