Uncertainty in Measurement and Calibration: what it is and how to calculate it

Uncertainty in measurement and calibration is the quantitative estimate that expresses the range within which the true value of a quantity varies, considering all sources of error in the calibration process. This value represents a certain probability that reflects confidence in the outcome. For example: Weight = (1.750 ± 0.001) kg, with a 95% probability. 

This concept is essential for the activities of the Quality sector. After all, accurate measurements are directly related to the quality of the product or service, the productivity of the team, and the competitiveness of your company in the market. Correctly evaluating and declaring this measurement and calibration uncertainty ensures that instruments meet performance requirements and are reliable for their intended use. 

However, for this to happen, it is necessary to have calibrated instruments that provide adequate measurements. Read on and find out more about the importance of measurement and calibration uncertainty in metrology. 

There is no 100% accuracy

No matter how good the instrument is and the conditions under which the measurement is performed, there will always be some uncertainty in the measured result. It can come from several factors: 

• As the instrument being used; 

• The person taking the measurement; 

• Environmental conditions; 

• The procedure used and many others. 

Therefore, being aware of the related uncertainty is essential to maintain the quality of the process and, consequently, of the products and services delivered. In addition, it is important to know that, to some extent, it is inevitable and is part of the calibration and verification process.

What is measurement and calibration uncertainty?

Uncertainty in measurement and calibration is the “size of doubt” that exists in each measurement. This manifests itself as a quantitative estimate of how much the true value of a quantity can vary over the course of the calibration process. 

Knowing this uncertainty, we can know how good a measurement is and decide whether it is suitable for a certain use. See a hypothetical and didactic case to illustrate this concept. 

Suppose you ask three people to measure a piece of string. They can use the instrument they want and the way they want. Three possible answers would be: 

• Person “A” says that the string is 90 cm. To reach this conclusion, he used a 30 cm plastic ruler; 

• Individual “B” concludes that the length of the string is 100 cm. He used a 3-meter tape measure to take the measurement; 

• Person “C” used a precision tape measure and reported that the string is 97.5 cm, with an uncertainty of 0.5 cm, plus or minus. She performed the procedure several times to calculate the average and find out the standard deviation. As a result, in addition to the measurement, it obtained the parameters that indicate its quality. 

It is not difficult to conclude that the answer of person “C” is much more reliable and complete. This example also shows how several factors can influence the measurement result. 

Types of measurement and calibration uncertainty

Measurement and calibration uncertainty is a parameter that quantifies the doubt associated with the result of a measurement, and this process is affected by several factors. Precisely because it is something so plural, this uncertainty also has different types. 

Below, you know the two most common: 

• Type A Uncertainty: It is uncertainty evaluated by statistical methods, based on data obtained from repeated measurements. 

• Type B Uncertainty: This type of measurement uncertainty is assessed through other means, such as information from calibration certificates, manufacturer manuals, or prior experience. 

Regardless of the type you are addressing, calibration is critical to identifying uncertainty and, in addition, to comparing an instrument’s measurements to a known standard to determine the accuracy of the instrument. It is during calibration that the measurement is calculated to provide a measure of the reliability of the calibration result. 

The Importance of calibration and uncertainty in measurement

Measurement uncertainty is crucial because it helps reduce errors, increases confidence in the results achieved, and protects the quality of the products/services offered by your company. 

Here are three of the top reasons to always keep an eye on measurement and calibration uncertainty. 

• Reliability: This care provides a measure of the reliability of the result of a measurement.  

• Comparability: Allows you to compare results from different measurements and thus determine whether the observed differences are significant or not.  

• Quality: As a result, it helps ensure the quality of products and services, especially in industries where accurate measurements are critical and there are diverse regulations.

Calculating uncertainty in measurement and calibration

Calculating measurement and calibration uncertainty involves several steps to ensure the accuracy and reliability of the results. They are: identification of sources of uncertainty; quantification of uncertainties; calculation of the combined uncertainty; Expanded uncertainty calculation and the result of measurement and calibration uncertainty calculation. 

Check out a summary of this process below to ensure that you will calculate correctly! 

1. Identifying Sources of Uncertainty

List all possible sources of uncertainty that can affect a given measurement. These factors can be, for example, the repeatability of the instrument, the resolution of the device, the environmental conditions, among others.

2. Quantification of Uncertainties

Identify whether each of your uncertainties is Type A (calculated using statistical methods and expressed as the standard deviation of the mean of the measurements) or Type B (evaluated based on information from third-party sources and usually expressed as a standard value).

3. Calculation of Combined Uncertainty

Once you have figured out the values of the uncertainties, combine the Type A and Type B uncertainties using the square root of the sum of the squares of the individual uncertainties.

4. Expanded Uncertainty Calculation

To find this value, multiply the combined uncertainty by the hedging factor—also called the spanning factor — represented by the symbol (k). It is chosen based on the desired confidence level (usually 95% or 99%). 

Measurement and calibration uncertainty calculation result

The measurement result is presented along with the expanded uncertainty, indicating the range within which the true value is expected to be at the specified confidence level. 

For example, if you measure a weight and find 1.750 kg with an expanded uncertainty of ±0.001 kg at 95% confidence, you would express the result as 1.750 ± 0.001 kg. 

Uncertainty in measurement is not an error

Finally, remember that uncertainty and error are two concepts that are sometimes confusing, but they are not the same thing. Error is the difference between the measurement performed by the instrument used by you and the measurement performed by the standard reference instrument. 

Uncertainty, on the other hand, is associated with the quality of the calibration or measurement performed and involves repeatability and predictability. 

See also: 7 strategies to extend the life of machines and equipment

Conclusion

Now that you know more about measurement and calibration uncertainty, ask yourself the following questions:

1. In my facility, the measurement processes look like which of the three examples we mentioned earlier (the one with the piece of string)?
2. Also, are the instruments you and your team use adequate and calibrated?
3. Are there methods and processes to perform the measurements, and, moreover, are these methods followed?
4. Do you know what uncertainty is involved in your measurements?
5. Are your calibration records centralized and organized? Is there efficient control over calibration deadlines and equipment traceability?
6. Can you easily/securely store and update calibration certificates, which are required in ISO 9001,   ISO/IEC 17025, and IATF 16949 audits?

If the answer is negative to any of these questions, you are probably using inappropriate results and, in this way, negatively affecting your quality, productivity and competitiveness.

The good news is that you can prevent this from happening in a very simple way: just use technology to have more efficiency and compliance in your operations! Our experts can help you identify the best strategies for your company with SoftExpert solutions. Contact us today!

FAQ 

What is measurement uncertainty? 

It is a quantitative estimate of how much the true value of a quantity can vary over the course of the calibration process. This quantitative estimate indicates the range in which the true value of a quantity can vary, considering all sources of calibration error, and expresses the level of confidence in the result (for example, 1.750 ± 0.001 kg with a 95% probability). 

Why is there always uncertainty, even with good instruments? 

Because factors such as the instrument itself, the operator, the environmental conditions, and the measurement procedure introduce inevitable variations in the result. 

What is the difference between measurement/calibration uncertainty and error? 

• Error is the difference between the measurement and the reference standard. 

• Uncertainty is the measure of doubt associated with measurement, reflecting repeatability and predictability. 

What are the two main types of uncertainty? 

• Type A: evaluated by statistical methods, based on repeated measurements (standard deviation). 

• Type B: Evaluated from external information (calibration certificates, manuals, experience). 

Why is calibration critical to uncertainty? 

Because it compares the instrument’s measurements with a known standard, allowing it to identify its inaccuracies and quantify uncertainty. 

What are the benefits of correctly declaring uncertainty? 

• Reliability: Provides security for the measurement result. 

• Comparability: allows you to distinguish significant differences between measurements. 

• Quality: ensures products/services are compatible with standards and regulations. 

What are the steps in calculating measurement uncertainty? 

1. Identification of sources of uncertainty (instrument, environment, operator). 

2. Quantification of each source as Type A or Type B. 

3. Calculation of combined uncertainty: square root of the sum of the squares of the individual uncertainties. 

4. Calculation of expanded uncertainty: multiplication of the combined uncertainty by the hedging factor (k), according to confidence level (e.g., 95%, 99%). 

5. Presentation of the result: measured value ± expanded uncertainty (e.g., 1.750 ± 0.001 kg at 95% confidence). 

How to interpret a value with uncertainty? 

It means that the true value is likely (e.g., 95%) to be within the range defined by the measured outcome plus or minus the expanded uncertainty. 

How do I know if my measurements are reliable? 

Make sure you: 

1. Use properly calibrated instruments. 

2. Adopt standardized methods and follow them. 

3. Record and control calibration deadlines and certificates (required in ISO 9001, ISO/IEC 17025, IATF 16949). 

What can indicate inappropriate use of measurement results? 

Negative responses to questions about calibration, procedures, known uncertainty, and records management can reveal inaccurate measurements that affect quality, productivity, and competitiveness.