In this chapter we describe how consistency and clarity may be brought to the calculation and expression of uncertainty in measurement.

The goal of any measurement is to establish a numerical value for the measurand. Depending on the accuracy that we wish to claim for the numerical value, the procedure that gives us the value may be relatively simple and direct, involving no more than a tape-measure, for example. In other situations the process may be more complicated, with several intermediate stages requiring the resources of a well-equipped laboratory. Thus, if the measurand is the width of a table, the tapemeasure is all that is needed. On the other hand, if the measurand is the accurate mass of an object, we need to know the value of the buoyancy correction (since the weight of the object is less by an amount equal to the weight of the volume of air that it displaces). This in turn requires knowledge of the volume of the object and of the density of air (which is a function of temperature, pressure and composition) at the time of measurement.

There are three components of a measurement: the measurand itself; the measuring instrument (which can be a stand-alone instrument such as a thermometer, or a complex system that occupies a whole laboratory); and the environment (which includes the human operator). The environment will, in general, affect both the measurand and the measuring instrument.