How to Chew Gum (Using the ISO Guide to Expression of Uncertainty in Measurement)

C.V. Gogolak1 and K.D. McCroan2 (1DHS Environmental Measurements Laboratory; 2EPA National Air and Radiation Environmental Laboratory)

The procedure for calculating uncertainties using ISO/GUM is straightforward: Step 1 - Identify the measurand and all the input quantities for the mathematical measurement model. Step 2 - Determine an estimate of the value of each input quantity. Step 3 - Evaluate the standard uncertainty for each input estimate using either a Type A or Type B method of evaluation. Step 4 - Evaluate the covariances for all pairs of input estimates with potentially significant correlations. Step 5 - Calculate the estimate of the measurand from the mathematical measurement model determined in Step 1. Step 6 - Determine the combined standard uncertainty of the estimate of the measurand. Step 7 - Optionally multiply the combined standard uncertainty of the estimate of the measurand by a coverage factor to obtain the expanded uncertainty in order to construct an interval that can be expected to contain the value of the measurand with a specified (high) probability. Step 8 - Report the result as the estimate of the measurand ± the expanded uncertainty, together with the unit of measurement, and, at a minimum, state the coverage factor used to compute the expanded uncertainty and the estimated coverage probability. Alternatively, report the result and its combined standard uncertainty with the unit of measurement. In practice it may not be obvious how to carry out these steps, or why they are necessary. Some of the concepts used in some of the steps, such as the propagation of errors, partial derivatives, sensitivity coefficients, Type A and Type B methods of uncertainty evaluation, the uncertainty budget, coverage factor, and the number of degrees of freedom may be unfamiliar or confusing. An example will illustrate how these steps can be easily performed in three different ways, first, by hand calculation, second, by use of GUM software and third by Monte Carlo.

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