Manipulating sensor data can deceive cyber-physical systems (CPSs), leading to hazardous conditions in physical plants. An Anomaly Detection System (ADS) like CUSUM detects ongoing attacks by comparing sensor signals with those generated by a model. However, physics-based methods are threshold-based, which can result in both false positives and undetectable attacks. This can lead to undetected attacks impacting the system state and potentially causing large deviations from the desired behavior. In this paper, we introduce a metric called transparency that uniquely quantifies the effectiveness of an ADS in terms of its ability to prevent state deviation. While existing research focuses on designing optimal zero-alarm stealth attacks, we address the challenge of detecting more sophisticated multi-alarm attacks that generate alarms at a rate comparable to the system noise. Through our analysis, we identify the conditions that require the inclusion of multi-alarm scenarios in worst-case impact assessments. We also propose an optimization problem designed to identify multi-alarm attacks by relaxing the constraints of a zero-alarm attack problem. Our findings reveal that multi-alarm attacks can cause a more significant state deviation than zero-alarm attacks, emphasizing their critical importance in the security analysis of control systems.
