Evaluation of Nonlinear and Polynomial Efficiency Models Based on Triple-to-Double Coincidence Ratio in Liquid Scintillation Counting

This study evaluates calibration models for the triple-to-double coincidence ratio (TDCR) method in liquid scintillation counting, focusing on the relationship between TDCR values and detection efficiency for 3 H and 14C. Four datasets were analyzed: three reconstructed from published literature and one obtained through original experimental measurements. A nonlinear core function (CF) model was compared with first- to third-order polynomial regressions. Model performance was assessed using root mean squared error (RMSE), mean absolute error (MAE), symmetric mean absolute percentage error (SMAPE), and the Akaike and Bayesian information criteria (AIC and BIC). While the CF model showed superior performance for 3 H due to its inherently nonlinear response, simpler polynomial models—particularly linear and quadratic— yielded comparable accuracy for 14C across all datasets. These models also enable analytical uncertainty propagation and offer greater numerical stability. The findings support a model selection strategy that emphasizes simplicity and parameter parsimony without sacrificing accuracy. This work highlights the practical advantage of selecting the least complex model that sufficiently captures the efficiency-TDCR relationship.