# Uncertainty Budgets and ISO 16063-21

## Back-to-Back Accelerometer Uncertainty Budgets

For any reader interested in expanding and calculating their own back-to-back accelerometer calibration uncertainty budget, ISO 16063-21 can provide an excellent reference point for equations and example calculations of uncertainty contributors. Beyond back-to-back vibration, the ISO 16063 group contains several other parts describing different methods of vibration and shock measurements. These parts range from basic concepts to calibration through earth’s gravitation to primary calibration using laser interferometry. As we have mentioned previously, it is important to be aware of the small details in the standards, such as part 21’s Clause 3.3 which highlights that the “limits” described in the standard may be exceeded, provided that the credibility of the measurement uncertainty is given its due diligence.

Uncertainty credibility can be achieved through the collection of Type A (random) empirical test data on your own measurement system along with analysis of Type B (systematic) uncertainty. It is important to remember that the empirical Type A dataset will give the true influence of a laboratory’s own unique environmental effects, acquisition noise, operators and others. Type A data gathering is an often overlooked exercise that could potentially shine a light on irregularities hiding in your measurement process. As stated in a previous article, the use of free resources such as the International Bureau of Weights and Measures’ (BIPM) " Guide to the Expression of Uncertainty in Measurement" (GUM) can be very helpful. The GUM contains valuable insight into the statistical analysis of data and the derivation of uncertainties.

No measurement is perfect. In metrology, we must remember that the true error of a measurement is unknown. Every measurement will have some range of uncertainty associated with it. It is only through the use of the tools in uncertainty analysis that we can help to ensure that the true measurement falls within the known bounds of our uncertainty in order to give our measurements significance.

To properly assess the uncertainty of a measurement system, you must also have a strong working knowledge of the system’s operation. This includes practical mechanical operation through electrical signal paths. Even signal analysis, as we have seen with the example of distortion in vibration calibration (discrete Fourier Transform vs. Root Mean Square) can play a big role in a system’s measurement uncertainty.

Just as knowledge of uncertainty is important in calibration systems, knowledge of a sensor’s performance capability can play a crucial role in practical vibration measurements. To achieve a meaningful measurement, one must not only know the uncertainty in the calibration of their sensors, but the effects due to the limitations in a sensor’s performance (effect of cable length on frequency response, amplitude linearity, mounting considerations, etc). For further useful resources at your finger tips, visit The Modal Shop’s Technical Library for a plethora of technical articles available for your perusal.