Design of the Hotelling $\mathrm{T}^{2}$ Control Chart for Anomaly Detection in IoT Systems

IoT systems such as smart homes or cities capture large amounts of data in real time using a wide range of interconnected sensor devices linked to edge nodes and their associated cloud services. In such systems, sensors must operate continuously and reliably in their deployed environment to deliver meaningful data to the users. As time passes, sensors may fail or become less effective in collecting raw data, resulting in erroneous data being delivered to the end user, who relies on their accuracy for decision-making. In this paper, we study detection methods of anomalies in sensor data based on Hotelling's <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$T^{2}$</tex> statistic. In simulation experiments, we calculate the lowest possible shift in data streams that are detectable by our proposed methods using sensor data from a smart home. Our results show that the proposed method successfully identifies the low shift in the means, given a confidence level with an accuracy of 90%. These results are based on data and do not assume a specific distribution, which opens up new potential applications for IoT data and anomaly detection. Additionally, some low shifts can be difficult to detect visually, but our proposed method will be able to detect those low shifts.