Measurement function

Introducing the uncertainty analysis tree

As we’ve seen, in most cases the measurand ( Y ) is not measured directly, but is instead obtained from a number of input quantities X_n via a mathematical relationship that we call the measurement function.

Importantly, whereas some of these input quantities are directly determined by measurement, parameterisation or data analysis, others are determined through their own measurement function of other input quantities. In other words, there can be a hierarchical aspect to uncertainty analysis.

To help organise a measurement-function centred analysis of uncertainty, it can be useful to prepare a graphical representation in the form of an uncertainty analysis tree, an example of which is shown below. On the next page, we’ll examine this diagram in more detail.