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Objectives: This article defines analytical performance specifications (APS) for evaluating laboratory proficiency through an external quality assessment scheme., Methods: Standard deviations for proficiency assessment were derived from Thompson's characteristic function applied to robust data calculated from participants' submissions in the Occupational and Environmental Laboratory Medicine (OELM) external quality assurance scheme for trace elements in serum, whole blood and urine. Characteristic function was based on two parameters: (1) β - the average coefficient of variation (CV) at high sample concentrations; (2) α - the average standard deviation (SD) at low sample concentrations. APSs were defined as 1.65 standard deviations calculated by Thompson's approach. Comparison between OELM robust data and characteristic function were used to validate the model., Results: Application of the characteristic function allowed calculated APS for 18 elements across three matrices. Some limitations were noted, particularly for elements (1) with no sample concentrations near analytical technique limit of detection; (2) exhibiting high robust CV at high concentration; (3) exhibiting high analytical variability such as whole blood Tl and urine Pb; (4) with an unbalanced number of robust SD above and under the characteristic function such as whole blood Mn and serum Al and Zn., Conclusions: The characteristic function was a useful means of deriving APS for trace elements in biological fluids where biological variation data or outcome studies were not available. However, OELM external quality assurance scheme data suggests that the characteristic functions are not appropriate for all elements., (© 2024 Walter de Gruyter GmbH, Berlin/Boston.)