This paper considers the well-known concept of uncertainty of a measurement result and discusses the mathematical approach adopted for its evaluation and expression by the present standard documents and, in particular, the Guide to the Expression of Uncertainty in Measurement. The practical limitations introduced by the assumptions of this mathematical approach are discussed, and the requirements of a new mathematical approach capable of overcoming the present limitations are drawn. A different mathematical approach, based on the theory of evidence and originally developed by the authors in recent years, is presented and discussed, with some new findings and observations

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In the measurement field, the correlation of two uncertainty contributions is a form of probabilistic association that can significantly affect the final uncertainty associated to the measurement result. The Guide to the expression of uncertainty in measurement recommends a mathematical approach to deal with correlated random contributions to measurement uncertainty. A similar kind of association, or dependence, can characterize also different systematic contributions to uncertainty and should be taken into account when evaluating their effect on the final measurement uncertainty. This paper discusses a new approach to handle such systematic contributions when they are represented by symmetric possibility distributions (PDs) of the same shape. This method allows one to build the joint PD of two systematic contributions, both dependent and independent, and propagate them through a generic measurement function.

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