Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

The Guidelines for Expressing Measurement Uncertainties and the 4:1 Test Uncertainty Ratio



Jun-Feng Song


In 1988, MIL-STD-45662A adopted the 4:1 Test Uncertainty Ratio (TUR); this was later incorporated into the ANSI/NCSL Z540-1 standard in 1994. However, in 1992, the National Institute of Standards and Technology (NIST) began to adopt a new method for evaluating and expressing measurement uncertainties. In a very short period of time other U.S. research and industrial institutions followed NIST's lead. This method uses the root-sum-of-squares (RSS) method for calculating the combined standard uncertainty from the Type-A and Type?B uncertainty components instead of simple arithmetic addition, and a coverage factor k=2 for calculating the expanded uncertainty (equivalent to two standard deviations) instead of the often-used three standard deviations in the U.S. The change from arithmetic addition to the RSS method has significantly reduced the calculated standard uncertainties. The change of the coverage factor from k=3 to k=2 further reduces the calculated expanded uncertainties by 33%. In many cases, the combined effects have caused a 50% or more reduction of calculated uncertainty from the same uncertainty budget. This has been documented in calibration and measurement reports. The reduced uncertainties have also caused significant increases of the actual TUR's for the same measurement processes and tolerance ranges. For many industrial institutions, the decreased uncertainty and increased actual TUR represent an improvement of our knowledge of the measurement uncertainties, rather than the real measurement quality improvements. When establishing the TUR for measurement quality control, the method used for calculating measurement uncertainty is an important consideration. Some examples are used for demonstrating the results of using different uncertainty methods for calculating measurement uncertainty and TUR from the same uncertainty budget.
Proceedings Title
NCSL Workshop & Symposium
Conference Dates
July 28, 1997
Conference Location
Atlanta, GA


customer's risk, producer's risk, TAR, Test Accuracy Ratio, Test Uncertainty Ratio, TUR, uncertainty


Song, J. (1997), The Guidelines for Expressing Measurement Uncertainties and the 4:1 Test Uncertainty Ratio, NCSL Workshop & Symposium, Atlanta, GA (Accessed April 15, 2024)
Created January 1, 1997, Updated February 19, 2017