For monitoring a data processing system, a sequence of critical conditions with increasing severity indexes is defined. Each critical condition is detected when a corresponding state parameter exceeds a threshold value with a predefined persistence over time. The persistence may be specified by a minimum number of repeated occurrences of this event, with a maximum number of consecutive non-occurrences that are allowed between them. Whenever critical conditions are detected, the monitoring application retrieves the severity index of the last detected critical condition with the highest severity index, and calculates an incremental index indicative of how closely the state parameter is approaching the next critical condition. An indicator of the health of the system may be generated by subtracting the severity index of the last critical condition plus the incremental index from an optimal value.