Uncertainty of Measurement

Metrology is defined by the International Bureau of Weights and Measures (BIPM) as "the science of measurement, embracing both experimental and theoretical determinations at any level of uncertainty in any field of science and technology." Other than the SI system, BIPM also maintains the standard documents, such as "Evaluation of measurement data — Guide to the expression of uncertainty in measurement". One may visit BIPM’s website (www.bipm.org) to download this document.

For industry, this document is also a very important foundation of many other standards, such as ISO 22514-7, ISO 10012:2003 and etc.. Therefore, not only for understanding the meaning of a report of a quantitative inspection, but also for implementing the right processes for QM according to the standards, it is worthy to read it and to have a basic idea of measurement uncertainty.

Every series of measurements has its distributed values (blue curve) around an average value which has an uncertain value (green arrow) against a real value (red line). And an operator of a measurement device or a report receiver has to always have the idea in mind that this distributed values and system deviation can never be compensated by any means. Therefore, if you just have a report issued by a national or international institute, the result will be "Y" - an expectation of results, "±U" - a range of the uncertainty, and "P%" - a confidence level. In other word, this institute can only provide you an "uncertain" result with a percentage of "confidence".


It might be surprising that a measurement costs quite some money, but there is no certain answer of it. So let us take a closer look at these concepts to understand the meaning behind them.

Expectation of results

The so-called average value is the expectation of measurement results.  


The uncertainty is an estimated value of random effects and imperfect correction of the result for systematic effects. For example, firstly, the institute calibrates the expectation as close as possible to the "real value" of a reference. However, this "calibration" process contains an uncertain value of the reference. And then when the measurement for your sample is performed, the results contain the uncertain value of the reference and an uncertain value of this measurement itself. Since the uncertain value is unknown, the concept of uncertainty as a range of value where the "real value" may arise with n% of possibility is used to define a random uncertain value. Hence, the standard deviation of results is used (not equal) to calculate the Type A uncertainty of measurement, and the uncertainty of the reference is used to calculate the Type B uncertainty. 

Confidence Level

By combining the Type A and B together, the uncertain value shall obey the distribution function with the combined uncertainty as its standard deviation. n% only means a possibility that a "real value" arise within one standard deviation range, but the P% on the report may be more than 99%. Therefore, to increase the possibility, a factor is multiplied to the combined uncertainty and the range is correspondingly expanded.