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Abstract A Bayesian multivariate approach to the evaluation of risks of false decisions on conformity of chemical composition of a substance or material due to measurement uncertainty is adapted to cases for which the composition is subject to a mass balance constraint. The constraint means that sum of the actual (“true”) values of the composition component contents under conformity assessment is equal to 1 (or 100 %) or another positive value less than 1 (less than 100 %). As a consequence, the actual values of the component contents are intrinsically correlated. Corresponding measured values of the component contents are correlated also. Any correlation can influence evaluation of risks of false decisions in conformity assessment of the substance or material chemical composition. A technique for appropriate evaluation of the relevant risks, including evaluation of the conformance probability of a subject or material composition, is discussed for different scenarios of the data modeling, taking into account all observed correlations. A Monte Carlo method is applied in the R programming language for the necessary calculations. Examples of evaluation of the risks are provided for conformity assessment of chemical composition of a platinum-rhodium alloy, pure potassium trioxidoiodate, a sausage, and synthetic air.
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