A probabilistic approach to measurement based decisions

Measurements are often an objective support for decision-making, in all fields, scientific, industrial or human-related. In this last case particular care has to be taken as a wrong decision can affect health, life or environment. In order to assess conformity of a critical process with legal prescriptions or with technical requirements, measurement uncertainty strongly affects the decisional process. In such cases, typically the state of the process under investigation is monitored by a set of measured parameters and their belonging to a given ‘‘safe’’ subset of the parameter space has to be checked. Common decision rules are based on expressing measurement results as intervals of values (expanded uncertainty), which results in an on–off acceptance criterion, with an uncertainty region. Alternatively, in order to obtain an explicit evaluation of the risk of taking the wrong decision, it is necessary to express the measurement result as a probability distribution. Due to the importance of the problem, in this article such an approach is addressed in general terms. A complete set of formulas for both uncertainty expression and risk evaluation are provided, their practicability is discussed and two prototype software packages, for supporting both uncertainty evaluation and risk assessment, are presented. Finally, some application examples, including scalar and vector measurements, are presented.