Calculation of measurement inaccuracy with the Monte-Carlo method

Measurements serve to gain information about a measurand. In general, this information cannot provide exact values of the measurand. Therefore before one gives this information in a responsible manner to others or uses it for oneself one has to quantify the incompleteness of that information. For that purpose one associates a measurement uncertainty with the result of a measurement. The ISO provide in their "Guide to the Expression of Uncertainty in Measurement" (GUM) [1] internationally agreed recommendations for the determination of measurement uncertainties associated with measurements. The GUM proposes a procedure for the propagation of uncertainties. Although only an approximation, this procedure is sufficient in praxis if certain conditions are met. In general, this is the case in praxis. The general solution for the problem "determination of measurement uncertainty" is found to be an integral which propagates probability distributions associated with measured input quantities. Using practical examples, this paper explains and derives this integral and discusses procedures for its solution, especially so the Monte Carlo method.