Assigned-Value Uncertainty in Limited-Participant Proficiency Testing: Monte Carlo Evaluation of ISO 13528 Estimators in an Industrial Calibration Scenario

In proficiency testing (PT), a consensus assigned value is an estimate whose uncertainty can affect participants’ performance classifications. This study evaluated the relationship between formula-based assigned-value uncertainty, empirical sampling variability and classification discordance under limited participation. Using gravimetric calibration of a 100 µL micropipette, 147.2 million Monte Carlo PT rounds were simulated across 1472 scenarios combining participant numbers (N = 5–50), two dispersion levels referenced to ISO 8655-2:2022 and outlier contamination (0–30%). The arithmetic mean and ISO 13528 Algorithm A were compared regarding assigned-value variability, uncertainty calibration, stability and classification. The 95th percentile of the assigned-value uncertainty ratio frequently exceeded the ISO 13528 threshold of 0.3, particularly under contamination and limited participation. This ratio was strongly associated with scenario-level decisional discordance (Spearman ρ = 0.97–0.99). Formula-based uncertainty exceeded empirical Monte Carlo variability for Algorithm A in all 1472 scenarios (calibration ratios of 1.044–1.301), whereas the arithmetic mean’s ratios ranged from 0.856 to 0.998. Although Algorithm A generally improved empirical stability under contamination, this advantage did not consistently translate into lower participant-number requirements under the combined acceptance criterion. These findings demonstrate that estimator robustness and uncertainty-formula calibration are distinct properties requiring separate evaluation when designing PT schemes with limited participation.