Statistical monitoring of atomic clocks: Applying Hotelling’s t-squared statistic and exponentially weighted moving average to caesium standards

Abstract

Ensuring the reliability of commercial caesium standards is essential, as anomalies in these atomic clocks can compromise critical systems that rely on precise timekeeping. Instabilities in caesium standards may lead to failures in satellite navigation, military communications, network synchronisation, and atomic time scales maintained by laboratories worldwide. Given their role as the foundation of atomic time, due to their high stability and precision, continuous monitoring of caesium standards is necessary to preserve signal integrity. This study applies statistical process control techniques to detect early signs of anomalous behaviour in caesium standards used in the Brazilian atomic time scale. Specifically, univariate and multivariate control charts are employed, including Hotelling's T² statistical test to identify deviations and determine their onset before a significant instability occurs. Additionally, an Exponentially Weighted Moving Average (EWMA) plot is used to monitor individual parameters within the multivariate framework. The results confirm abnormal behaviour in one of the standards and precisely pinpoint the moment the anomaly begins, demonstrating the effectiveness of the combined use of Hotelling's T² and EWMA methods.