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Calculation of the uncertainty of the mean of autocorrelated measurements

Published

Author(s)

Nien-Fan Zhang

Abstract

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.
Citation
Metrologia

Keywords

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

Citation

Zhang, N. (2006), Calculation of the uncertainty of the mean of autocorrelated measurements, Metrologia, [online], https://doi.org/10.1088/0026-1394/43/4/S15 (Accessed June 25, 2024)

Issues

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Created August 4, 2006, Updated June 7, 2024