Methods and apparatus are provided for analyzing a complex system that includes a number of subsystems. Each subsystem comprises at least one sensor designed to generate sensor data. Sensor data from at least one of the sensors is processed to generate binary evidence of a sensed event, and complex evidence of a sensed event. The complex evidence has more sophisticated mathematical properties than the binary evidence. The complex evidence comprises one or more of: a condition indicator (CI), a health indicator (HI), and a prognostic indicator (PI). A system fault model (SFM) is provided that defines statistical relationships between binary evidence, complex evidence, and an underlying failure mode (FM) that is occurring in the complex system. The binary evidence and the complex evidence are processed to identify failure modes taking place within one or more of the subsystems. Based on the binary evidence and the complex evidence and the SFM, diagnostic conclusions can be generated regarding adverse events that are taking place within the complex system, and prognostic conclusions can be generated regarding adverse events that are predicted to take place within the complex system.