# What is Uncertainty in Measurement (Measurement Uncertainty)?

You may have heard the terms measurement uncertainty when calibrating your caliper with gauge blocks. In other words, wringing more gauge blocks can contribute more to the measurement uncertainty. The same thing goes with when using the workshop grade gauge blocks, it has more uncertainty compared to the master grade ones.

How that could be? What does actually this term mean?

If you wonder how accurate your instrument is, then learning uncertainty is a must for a deep understanding of accuracy.

## Uncertainty in Measurement According to Metrology

Before going further, it is better to know the meaning of uncertainty of measurement based on the definition given by the International Vocabulary of Metrology.

According to the International Vocabulary of Metrology – Basic and General Concepts and Associated Terms (VIM), measurement uncertainty, the uncertainty of measurement, and uncertainty is:

“non-negative parameter characterizing the dispersion of the quantity values being attributed to a measurand, based on the information used”

While measurand, according to the same source (the International Vocabulary of Metrology – Basic and General Concepts and Associated Terms) is:

“quantity intended to be measured”

On the other hand, the definition of the uncertainty of measurement according to JCGM 100:2008 Evaluation of measurement data — Guide to the expression of uncertainty in measurement which was also derived based on VIM is:

“parameter, associated with the result of a measurement, that characterizes the dispersion of the values that could reasonably be attributed to the measurand”

From these definitions, we can simply say that uncertainty can be a characteristic of the measurement process determined from the analysis of the measurement results of the quantity being measured.

## Uncertainty in Measurement Simply Explained

These definitions may be very technical but there is also a simple way to explain the meaning of the uncertainty of measurement by focusing on the words: uncertainty and measurement.

From the word itself, uncertain, which means, not sure, not confident, can’t be exactly sure, and there is a doubt. It can simply define uncertainty of measurement as the doubt in measurement.

Measurement is the process or method that we take to obtain the value of a measurand (quantity to be measured). And surely, our senses (eyes, nose, etc) may feel it such as distance (short/long or close/far) but cannot express it in a particular number. That said, that measurement must employ a measuring device or measuring instrument to get the value.

However, that instrument itself may be poorly manufactured or of low quality. So, you cannot trust it at all. The measurement result may be misleading. That’s only from the point of quality. What if the quality of the instrument is good? Still, it contains uncertainty, that comes from external sources.

The rise of temperature may expand the object materials, so you are measuring that object when its length has been extended. You position the dial indicator at a certain angle which leads to a certain cosine error. A low-quality caliper that leads to abbe error can contribute to uncertainty. And many more.

When something can’t be/is not perfect even if it is done in a standard process, there will always be doubt. However, the value may be larger or smaller depending on how many uncertainty sources that involve.

Precision and accuracy are determined by knowing the uncertainty of measurement. This is only one reason why uncertainty of measurement is important, and it is the simplest example to better understand the meaning of measurement uncertainty.

Measurement uncertainty is often disregarded depending on the need. A school student doesn’t need to know the uncertainty value of the object length measurement with a ruler. In contrast, as the commercial industries and technology continuously emerge, a need for strict measurements are required which are met by a more strict measurement process.

## What are the Possible Causes of Uncertainty of Measurement?

To know the factors causing the uncertainty of measurement, try not to be confused between error and uncertainty. As discussed above, a measurement cannot be perfect, and in order to know the reason, an investigation and analysis should be conducted.

For example, a 22 mm diameter pipe is used for the industrial production of a machine. During the inspection, the actual diameter of the pipe measured by the inspector using a caliper is 21.95 mm. In fact, the true value of the diameter is 22 mm, although the measured value is 21.95 mm.

The difference between the true value and the actual measured value is called the error. Simply, the error of measurement is -0.05 mm.

Upon rechecking the pipe using the same measuring device, wherein 5 times repeated measurement was conducted by the same inspector, the measured value is not the same. The results of the measurements are 21.95 mm, 22.03 mm, 22.02 mm, 21.98 mm, and 21.97 mm. From this example which you can also try for any parts that you have and a measuring instrument, there are times that you will get different results.

If you are experiencing such varying values, you need to investigate the case and evaluate the measurement. It might be some errors that only needs corrections. In some cases, there is a need for the measurement uncertainty to be computed in order to check how close to the true value the measurement should be.

Listed below are some of the factors that you need to consider to get the uncertainty of your measurement when you conduct your evaluation and investigation. Although these error and uncertainty sources may be inevitable, it is also advisable to take caution and reduce measurement uncertainty as much as possible.

### 1. Man/Operator

Manpower is always an uncontrollable variable that must always be considered during the measurement process. We, humans, are very prone to error. Some errors caused by the operator can be corrected and some that cannot be corrected are due to uncertainty. Different operators have different levels of skills, expertise, and knowledge which affects the measurement result. Usually, a Gauge R&R or repeatability and reproducibility tests are conducted to get the measurement uncertainty due to manpower.

### 2. Measuring Devices/Instruments/Equipment

When conducting measurement, select the best-fit measuring device or instrument. These instruments should have certificates wherein uncertainty of measurement is already indicated. During a long time use of measuring instruments, they may wear which will contribute to error.

### 3. Calibration Uncertainty

Another source of uncertainty is the calibration uncertainty of measuring instruments. You are using a working standard. A working standard in the workshop has greater uncertainty compared to a calibration lab standard. The greater the uncertainty, the lower the accuracy.

### 4. Measurement Method

The measurement process sometimes are consist of different methods. As an example, calibrating a micrometer with two gauge blocks that need to be wrung. The individual gauge blocks already have uncertainty as well as the wringing process also generates uncertainty. Both these uncertainty sources need to be considered. Therefore the measurement process should be evaluated carefully, especially those that have combined processes.

### 5. Environment

Environmental factors such as temperature and humidity contribute to uncertainty in measurement.

## How to Calculate, Evaluate and Express the Uncertainty of Measurement?

Uncertainty of measurement based on its definition is a non-negative parameter, therefore there might be some formula and technique to get this non-negative parameter.

The step-by-step process of calculation of the measurement uncertainty will not be discussed here. We can refer there is a technique recommended by the International Organization for Standardization (ISO) and International Bureau of Weights and Measures or Bureau International des Poids et Mesures (BIPM) that you can search online called the GUM: Guide to the Expression of Uncertainty in Measurement. Not only the calculation but also the proper evaluation, and expression of measurement uncertainty are discussed there.

Some of the key points of the GUM to evaluate and express the measurement uncertainty are listed below.

## Evaluation of Measurement Uncertainty

According to GUM, the main stages of the uncertainty evaluation are formulation and calculation, and, propagation and summarizing.

1. During the formulation stage, study your input quantity and determine what measurement model you need to have an output quantity. You must need to determine the necessary result from the measurement process.
2. During the calculation and propagation stage, perform the needed analytic methods, or the mathematical analysis, probability, etc. for the standard uncertainty, combined standard uncertainty, and expanded uncertainty.
3. Check the results. If there is a need to perform added calculations especially if other sources of uncertainty were not considered.
4. Finalize the calculation results.
5. Present the results. Rules for presenting the results are also indicated on the GUM.

## Expressing Measurement Uncertainty

Here is one way how to say the measurement result with uncertainty.

Remember the previous mentioned example about the measured pipe diameter. The measurement result can be written like this:

22mm ± 0.05 , at a confidence level of 95%

or, it can be expressed as:

At a 95% confidence level, the diameter of the pipe is between 21.95mm and 22.05mm.

From this expression, do not be confused between tolerance and uncertainty. They may look alike but they are totally different.