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The Guide to the Expression of Uncertainty in Measurement (usually referred to as the GUM) provides the basic framework for evaluating uncertainty in measurement. The GUM however does not always provide clearly identifiable procedures suitable for medical laboratory applications, particularly when internal quality control (IQC) is used to derive most of the uncertainty estimates. The GUM modelling approach requires advanced mathematical skills for many of its procedures, but Monte Carlo simulation (MCS) can be used as an alternative for many medical laboratory applications. In particular, calculations for determining how uncertainties in the input quantities to a functional relationship propagate through to the output can be accomplished using a readily available spreadsheet such as Microsoft Excel. The MCS procedure uses algorithmically generated pseudo-random numbers which are then forced to follow a prescribed probability distribution. When IQC data provide the uncertainty estimates the normal (Gaussian) distribution is generally considered appropriate, but MCS is by no means restricted to this particular case. With input variations simulated by random numbers, the functional relationship then provides the corresponding variations in the output in a manner which also provides its probability distribution. The MCS procedure thus provides output uncertainty estimates without the need for the differential equations associated with GUM modelling. The aim of this article is to demonstrate the ease with which Microsoft Excel (or a similar spreadsheet) can be used to provide an uncertainty estimate for measurands derived through a functional relationship. In addition, we also consider the relatively common situation where an empirically derived formula includes one or more 'constants', each of which has an empirically derived numerical value. Such empirically derived 'constants' must also have associated uncertainties which propagate through the functional relationship and contribute to the combined standard uncertainty of the measurand.

The Evaluation of Measurement Data - Guide to the Expression of Uncertainty in Measurement (usually referred to as the GUM) provides general rules for evaluating and expressing uncertainty in measurement. When a measurand, y, is calculated from other measurements through a functional relationship, uncertainties in the input variables will propagate through the calculation to an uncertainty in the output y. The manner in which such uncertainties are propagated through a functional relationship provides much of the mathematical challenge to fully understanding the GUM.The aim of this review is to provide a general overview of the GUM and to show how the calculation of uncertainty in the measurand may be achieved through a functional relationship. That is, starting with the general equation for combining uncertainty components as outlined in the GUM, we show how this general equation can be applied to various functional relationships in order to derive a combined standard uncertainty for the output value of the particular function (the measurand). The GUM equation may be applied to any mathematical form or functional relationship (the starting point for laboratory calculations) and describes the propagation of uncertainty from the input variable(s) to the output value of the function (the end point or outcome of the laboratory calculation). A rule-based approach is suggested with a number of the more common rules tabulated for the routine calculation of measurement uncertainty.