IUPAC/CITAC Guide: Evaluation of risks of false decisions in conformity assessment of a multicomponent material or object due to measurement uncertainty (IUPAC Technical Report)

Risks of a false decision on conformity of the chemical composition of a multicomponent material or object due to measurement uncertainty are defined using the Bayesian approach. Even if the conformity assessment for each particular component of a material is successful, the total probability of a false decision (total consumer’s risk or producer’s risk) concerning the material as a whole might still be significant. This is related to the specific batch, lot, sample, environmental compartment, or other item of material or object (specific consumer’s and producer’s risks), or to a population of these items (global consumer’s and producer’s risks). A model of the total probability of such false decisions for cases of independent actual (‘true’) concentrations or contents of the components and the corresponding measurement results is formulated based on the law of total probability. It is shown that the total risk can be evaluated as a combination of the particular risks in the conformity assessment of components of the item. For a more complicated task, i.e. for a larger number of components under control, the total risk is greater. When the actual values of the components’ concentrations or contents, as well as the measurement results, are correlated, they are modelled by multivariate distributions. Then, a total global risk of a false decision on the material conformity is evaluated by the calculation of integrals of corresponding joint probability density function. A total specific risk can be evaluated as the joint posterior cumulative function of actual property values of a specific item lying outside the multivariate specification (tolerance) domain when the vector of measured values obtained for the item is inside this domain. The effect of correlation on the risk is not easily predictable. Examples of the evaluation of risks are provided for conformity assessment of denatured alcohols, total suspended particulate matter in ambient air, a cold/flu medication, and a PtRh alloy.