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Difficulties arising from the representation of the measurand by a probability distribution

This paper identifies difficulties associated with the concept of representing fixed unknown quantities by probability distributions. This concept, which we refer to as the distributed-measurand concept, is at the heart of the approach to the evaluation of measurement uncertainty described in Supplement 1 to the Guide to the Expression of Uncertainty in Measurement. The paper notes (i) the resulting lack of invariance of measurement results to nonlinear reparametrizations of the measurement problem, (ii) the potential undetected divergence of measurement estimates obtained by Monte Carlo evaluation, (iii) the potential failure of the methodology to give uncertainty intervals enclosing the values of the measurands with an acceptable frequency and (iv) the potential loss of measurement precision. The distributed-measurand concept is gaining popularity partly because of its association with analysis using the Monte Carlo principle. However, the Monte Carlo principle is also applicable without adopting the distributed-measurand concept. Accordingly, an alternative approach to the evaluation of measurement uncertainty is briefly described.