*2.1. Univariate Real Quantity*

1. The formulation stage involves the following steps:


$$\mathbf{Y} = f(\mathbf{X}).$$

	- Assign a number *M* of trials.
	- For *k* = 1, ... , *M*, sample values *x*1,*k*, ... , *xN*,*<sup>k</sup>* from the probability distributions for the input quantities and evaluate

$$y\_k = f(\mathbf{x}\_{1,k}, \dots, \mathbf{x}\_{N,k}).$$


Note that, both for simplicity and to reflect the choice of examples in Section 4, this section considers only the case of a measurement model that can be classified as explicit, i.e., the measurand can be expressed as an explicit mathematical function of the input quantities. Variants of MCM are available for the case where the relationship between the measurand and input quantities cannot be expressed explicitly. The storage within DCCs of uncertainty information obtained using MCM is equally applicable to explicit and implicit measurement models. In addition, again for simplicity, this section considers a particular implementation of MCM where a fixed number *M* of trials is assigned in the first step. Alternative applications of MCM can, and possibly should, be implemented, e.g., an adaptive approach as described in clause 7.9 of GUMS1 [7] where an increasing number of trials are carried out until results are deemed to have stabilised sufficiently according to predetermined criteria.
