Measurement uncertainty expresses the spread of the values associated with a measurement result. The uncertainty reflects incomplete knowledge about the result. A measurement result is therefore an interval of probable values. It is important to be able to define the variables that create uncertainty. This is an area of expertise for the Norwegian Metrology Service. You are the experts in your field – our goal is to strengthen your insight into your own measurement methods.
No measurement is entirely exact. It may depend on the measurement system, procedure, operator, environment, and other factors. Anyone who uses or relies on a measurement result should understand more than just the result itself – they should also understand the background: why the result turned out as it did, what traceability it has, and why that particular method was used. And most importantly – by understanding the measurement result, you can also defend it.
In a calibration certificate, a measurement uncertainty is always stated for the measurement result. The uncertainty is most often presented as a symmetric interval around the result, as follows:
Measurement result ± measurement uncertainty
The measurement uncertainty is calculated as a 95% confidence interval. This means there is a 95% probability that the true value of the measured quality lies within this interval.
Example:
The length of a particular gauge block is 2000 mm ± 1 mm. There is therefore a 95% probability that the block is between 1999 mm and 2001 mm.
The method for calculating measurement uncertainty follows document EA-4/02, which is based on the ISO Guide to the Expression of Uncertainty in Measurement (GUM). In brief, the method involves setting up an uncertainty budget for the measurement. The budget contains two main elements:
It is important that the measure is clearly defined. A good description with sketches or diagrams may be necessary. Each source of uncertainty must be assessed – whether by statistical methods, information from other calibration certificates, or scientific judgement. The magnitude of each uncertainty component must be determined, and its influence on the measured quality evaluated. Each source should be specified, and possible correlations considered. All sources of uncertainty are then combined, and the combined uncertainty is expanded to obtain an approximately 95% confidence interval.
Because everything must be documented and explained in detail, the uncertainty budget can also be seen as an uncertainty budget. The term budget, however, implies that it applies to future measurements. Occasionally, poor measurement objects may mean that the planned budget is not achieved – the uncertainty budget will then show that the measurement uncertainty became somewhat greater than expected.
For calibration of gauge blocks by comparison, an excellent example of an uncertainty budget can be found in EA-4/02, supplement part 1.
This example shows how, by introducing new variables, the measurement function can be rewritten so that none of the input quantities are correlated.
In this PDF, (in Norwegian) the Norwegian Metrology Service demonstrates how, through practical experiments, we have evaluated the effects of temperature in gauge block calibration by comparison. These measurements form the basis for the choices made in our calibration procedure and how gauge blocks are handled in practice. Typical waiting times for temperature stabilisation of gauge blocks have also been determined from these measurements.
Please contact us if you would like more information about the course.
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