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.

Calculation of the uncertainty of the mean of autocorrelated measurements



Nien-Fan Zhang


When repeated measurements are autocorrelated, it is not appropriate to use the traditional approach to calculate the uncertainty of the average of the measurements, which assumes that the measurements are statistically independent. In this paper, we propose a practical approach to calculate the corresponding uncertainty and the confidence interval when the data are from a stationary process. For illustration, the approach is applied to two examples: linewidth measurements made by a scanning electron microscope and weight measurements. The results are also extended to the general case in which both Type A and Type B uncertainty components are presented and to the case of weighted means.


autocorrelation function, autoregressive process, confidence interval, stationary process, time series


Zhang, N. (2006), Calculation of the uncertainty of the mean of autocorrelated measurements, Metrologia, [online], (Accessed June 25, 2024)


If you have any questions about this publication or are having problems accessing it, please contact

Created August 4, 2006, Updated June 7, 2024