What is Measurement Uncertainty?

measurement uncertainty

Measurement uncertainty is the expression of the statistical dispersion of the values attributed to a measured quantity. It is an inherent part of any measurement process, quantifying the doubt concerning the measured value.

Recognizing that every measurement is subject to some error, measurement uncertainty ensures that the measurement result is accompanied by a complete statement of this uncertainty, often expressed as a standard deviation. This concept serves as a reminder that no measurement can be considered perfect. 

Understanding and applying the principles of measurement uncertainty is crucial for interpreting results accurately. It allows for a better assessment of measurement reliability, which is essential for decision-making, compliance with industry standards, and maintaining a high level of integrity. As such, measurement uncertainty has implications for scientific research,  technological development, quality control, and beyond.


Key Standards and Guides

Measurement uncertainty is guided by internationally recognized standards and guides. The seminal document is the Guide to the Expression of Uncertainty in Measurement (GUM), which outlines the framework for expressing uncertainty. GUM provides a standardized methodology for evaluating and stating uncertainty, ensuring consistency and understanding across diverse fields and applications.

Furthermore, the International Organization for Standardization (ISO) and the International Electrotechnical Commission (IEC) maintain ISO/IEC 17025, which includes requirements for the calibration and testing of laboratories concerning the reporting of measurement uncertainty. This helps labs improve the accuracy of their results and provides a basis for the comparison of measurement capabilities globally. Additionally, national and international metrological organizations often publish complementary guides, providing industry-specific guidelines on the practical application of these standards.


Quantifying Uncertainty

Quantifying uncertainty involves statistical methods and practical applications, with the aim of determining standard measurement uncertainty and relative uncertainty.

In statistics, the standard deviation is the dispersion of a dataset relative to its mean. It is a critical component in calculating uncertainty. For a set of data, standard deviation indicates how much individual data points deviate from the average value or the mean. Variance, the square of the standard deviation, quantifies the spread of data points.

Standard uncertainty is used to quantify measurement uncertainty, which is derived from the standard deviation of a series of repeated measurements. Knowing the standard uncertainty enables one to calculate the expanded uncertainty by multiplying it by a coverage factor, which is based on the probability distribution. This expanded uncertainty helps to create a coverage interval likely to encompass the true value.


Uncertainty in Practice 

Calibration is important because it ensures that instruments provide accurate data. The uncertainty related to calibration forms part of the total measurement uncertainty. Metrology data is often represented with relative uncertainty—a dimensionless measure that compares the standard uncertainty to the absolute value of the measurement.

Measurements accompanied by a statement of uncertainty inform about the quality and reliability of the data. For example, when measurements have a high standard deviation, the uncertainty is large, implying that there may be a significant variation in the observed data. On the other hand, a low standard deviation suggests less variability and, thus, a lower standard uncertainty.

Measurements should be reported with a probability distribution that best describes the uncertainty and how it propagates through calculations. These distributions, whether normal, uniform, or otherwise, are fundamental to determine the coverage interval where the true value is expected to lie with a certain probability.


Measurement Procedures and Calibration

Precision and accuracy in measurement procedures, along with rigorous uncertainty analysis, form the cornerstone of trustworthiness in the results obtained from a measuring instrument.

Calibration laboratories use detailed measurement procedures to ensure the highest degree of accuracy and precision. Within these laboratories, uncertainty analysis is paramount to the calibration process. It identifies all potential sources of error—ranging from the environment to the measuring system itself—and quantifies their impact on the measurement.

Each variable in a measurement procedure is scrutinized for its contribution to the overall uncertainty, reinforcing the credibility of measurements. Calibration assures the adequacy of the measuring system for its intended application, linking measurements to national or international standards.