I have empirically developed a sensor failure detection system which works fine. The system receives inputs from different types of sensors. Because of noise characteristics, I use low pass filters on some sensors output. In the system, all these sensor readings form a signal which is constantly compared with a model and in the end create a remainder signal. In case of a sensor failure, the remainder signal violates pre-defined thresholds and raise an alarm.
For the system analysis, I use superposition law, meaning that except one, all inputs are considered zero and a step signal is propagated through the system. Here the step signal represents a sensor failure. With various approximations, I am able to get the corresponding transfer functions. That way, I can justify the system performance. However, this has raised lots of ambiguities. I am asked to justify and optimize the system performance (with the simultaneous consideration of all inputs) through time or frequency analysis. The result can be a frequency response or a mathematical equation or other system performance representations.
My questions: Since I am dealing with a relatively complex, nonlinear system, is there any way to analyze and optimize its performance with the simultaneous consideration of all inputs/sensor readings? Is there some good literature that I can study this topic from?