We consider a probabilistic model of the measurement process, based on identifying two main sub-processes, named observation and restitution. Observation constitutes the transformations involved in producing the observable output. Restitution constitutes the determination of the measurand (the quantity measured) from the observable output, and includes data processing. After providing a probabilistic representation of the observation sub-process, we derive appropriate formulae for addressing restitution and describing the overall measurement process. The model allows the treatment in probabilistic terms of both the random and systematic effects that influence the measurement process, and may prove particularly useful in the formulation phase of uncertainty evaluation. We also discuss the different ways in which the measurand can be characterized by a probability distribution, and demonstrate the application of the approach to the analysis of risk in conformance testing.
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