One embodiment provides a system that analyzes telemetry data from a monitored system. During operation, the system periodically obtains the telemetry data as a set of telemetry variables from the monitored system and updates a multidimensional real-time distribution of the telemetry data using the obtained telemetry variables. Next, the system analyzes a statistical deviation of the multidimensional real-time distribution from a multidimensional reference distribution for the monitored system using a multivariate sequential probability ratio test (SPRT) and assesses the integrity of the monitored system based on the statistical deviation of the multidimensional real-time distribution. If the assessed integrity falls below a threshold, the system determines a fault in the monitored system corresponding to a source of the statistical deviation.