# Calculating measurement uncertainty – you need to pay attention to this

Measurement uncertainty is of great economic importance. The measurement uncertainty is decisive for the level of testing costs. Even small measurement uncertainties can lead to high testing costs.

It is therefore all the more important to know how the measurement uncertainty is calculated and which factors influence it.

Here you can find out which methods you can use to determine the measurement uncertainty, how you can reduce the measurement uncertainty and how you can keep an eye on the causes of the measurement uncertainty.

## How the measurement uncertainty is determined

The measurement uncertainty is determined by means of experimental procedures, also known as measurement series. Various other methods are also used.

In these procedures, the causes are identified and indicated in a numerical value.

These causes are then summarized in a so-called measurement uncertainty budget.

A model is created, so to speak, which determines the overall measurement uncertainty.

Comparable measurement results are essential in the field of calibration and measurement technology. For this reason, standardized procedures are necessary when determining the measurement uncertainty.

## Interpret measurement uncertainty and reduce testing costs

Knowledge of measurement uncertainty forms the basis for comparing and accepting measurement results.

Knowledge is therefore extremely important. Sound testing and calibration decisions cannot be made without knowledge of the measurement uncertainty.

Please refer to the “Golden Rule of Metrology”.

This means that the ratio of measurement uncertainty to tolerance should not exceed 10%.

This will give you an initial indication. You can decide how suitable a particular measurement process is for a specific application.

The measurement uncertainty also determines how you design and monitor certain measurement processes.

Ensure a sensible ratio of tolerance, production spread and measurement uncertainty. This creates the conditions for economical production.

Unnecessarily precise measurements drive up your inspection costs, but a measurement process with high measurement deviations increases your error costs.

Decide on the right ratio to reduce your testing costs.

## Causes of measurement uncertainty

There are basically five different causes. Each of these has a different influence on the measurement deviation.

A distinction is also made between random and systematic measurement deviation. The random measurement deviation cannot be influenced.

At best, this can be estimated using mathematical-statistical methods.

The systematic measurement deviation is made up of the known or unknown influencing factors. Known factors are added together. Unknown influencing factors are treated as random measurement deviations.

All components must be taken into account so that the measurement deviation can be calculated as accurately as possible.

The relationships between the various influencing factors must be understood as well as possible. Therefore, the determination of measurement uncertainty requires extensive knowledge and experience of random and systematic measurement deviations.

All causes of measurement uncertainty are also dependent on the methods and measuring devices used for calibration.

The five basic causes are explained in more detail below.

### Surroundings

An important factor in the environment is the temperature. This can influence measurements.

Temperature deviations from the reference temperature or temperature fluctuations during the measurement ensure this.

Temperature changes are also noticeable, for example, in the linear expansion of measuring equipment. If the temperatures are measured continuously, you can take them into account in your measurement by making a corresponding correction in the measurement result.

Humidity can also influence the measurement result, especially with optical measurements.

Why?

Air has a refractive index. The humidity in the air influences this refractive index. If the humidity changes, this affects the refractive index, which in turn influences the measurement result of optical measurements.

Vibrations are partly generated by the environment, but also by the respective measuring device. Seismic vibrations can be reduced by foundations and other vibration-damping measures.

Soiling must also be taken into account. Contaminated measuring equipment usually causes deviations in shape and position.

You should therefore ensure that your measuring equipment is cleaned thoroughly and regularly.

### Measuring device

The design of the measuring device to be used is particularly important.

This has a decisive influence on the deformation. Deflection due to dead weight or the weight of workpieces influences the measurement result.

The measuring standard used for the measurement must also be taken into account when determining the measurement uncertainty. These dissolve over time, causing deviations in the measurement.

It is important for the evaluation software to use certified sample data with input and result data. Otherwise, imperfect algorithms can have an impact on the measurement uncertainty.

### Material

The material you use has many properties.

Density, elasticity, hardness and many other factors influence the measurement uncertainty.

Deformation of the material is caused by the dead weight of clamping forces and by one-sided heating.

Therefore, support your material with suitable workpiece holders and select their support points favorably in order to keep the deformations as small as possible.

### Users

The calibration or measurement technician usually has the greatest influence on the measurement result. It is crucial that it interprets the measurement task correctly.

Measurement technicians must be well trained to reduce any influences.

The choice of clamping is the first decisive point. Workpieces with a large length/cross-section ratio, for example, should be supported in such a way that they bend as little as possible due to their own weight.

The measurement process also plays a major role. The measurement result is positively influenced by a clever choice of measurement procedure.

Of course, people sometimes make mistakes. Subjective influences are therefore also possible. This includes reading or transmission errors. However, careful, experienced and trained working methods reduce these errors.

### Measurement strategy

Measuring equipment, auxiliary equipment and the type of measurement are defined in a measurement strategy.

Clamping devices, lighting and positioning devices can influence the measurement uncertainty. Both positive and negative.

Select your tools to support the measurement process and thereby reduce measurement uncertainty.

The measurement procedure defines the principle and method of measurement. Physical principles are defined here. It is also decided whether the measurement is relative or absolute.

The evaluation strategy determines the association procedure used. This is an essential criterion for determining functional measurement results. This therefore has a decisive influence on the measurement uncertainty. Here you can also specify whether any measuring points are filtered and which parameters are used for these filters.

## Conclusion

The influences and causes of measurement uncertainty therefore consist of a large number of factors. To calculate the measurement uncertainty, all components must be taken into account.

Therefore, proceed step by step:

• List all relevant influencing variables
• Create a model with which you can determine the measurement uncertainty
• Determine the influence of the individual influencing variables
• Summarize the influences to a combined standard measurement uncertainty
• Specify the determined measurement uncertainty