Monitoring data often need deep analysis in order to understand the real behaviour of a structure or a soil mass which may be overshadowed by unknown phenomena or boundary conditions. Temperature is one of the most common parameters which affect field measurements and create problems in data interpretation and use. The present work introduces a statistical approach for better understanding the behaviour of the monitored phenomena, reducing the uncertainty associated with the measurements and detecting possible anomalies in the monitoring system. The approach is described with reference to a specific application on a cable stayed bridge. In order to describe the dynamics of the bridge in normal conditions, a state space model is proposed. Then, a hierarchical multivariate detector (HMD), based on a Multivariate Exponentially Weighted Moving Average control chart (MEWMA), is introduced for analysing the behaviour of the monitoring system when one or more parameters change. Using appropriate threshold values, the HMD is able to check the tendency of the system to change its status from a safe situation to a warning or alert one and to localize the source of variability. In order to show its ability to detect anomalies, some simulation examples are provided.