In recent years, stochastic detectors have gained prominence in networked systems for anomaly detection. These detectors have demonstrated advantages over their traditional counterparts, particularly in safe-guarding against data integrity attacks targeting state estimation. Despite these advancements, the impact of the detector on alarm performance-such as alarm-triggering rates at normal conditions-remains under-explored, especially in scenarios where delay timers are applied to the raw alarm sequence. This study delves into the monitoring of a correlated Gaussian process variable using stochastic detectors. An explicit formula for the alarm performance is given, highlighting how it is influenced by the duration of delay timers. The efficacy of the proposed approach is validated through numerical examples and a simplified process model.