The assessment of the accuracy of a weigh-in-motion (WIM) system is described in this paper. It is based on a statistical composite hypothesis test for which the Type I error is the supplier risk for the WIM system. This statistical test is built in the asymptotical setting, namely for large samples of measurements, with an implicit estimator of the tolerance. Considering an observation sample of independent and identically distributed relative errors, this procedure is used in the classical WIM assessment method described in the COST 323 action and compared to the classical estimator of the tolerance. The test also gives formulæ to practitioners implying the observation sample size comparing to the usual estimator for which the observation sample size is tabulated. An application on a bridge-WIM system is also done.