Pair monitoring of redundant technical systems

We pose and solve the deterministic problem of simultaneous technical condition monitoring in real time for both the main (functional) and control (monitoring) parts of the system. We propose an approach based on a logical analysis of the results of the built-in control for a pair of comparable technical devices, which are in the general case heterogeneous in their manufacturing and infrastructural support. We obtain the structure and rules for the construction of the indicator matrix that allows to divide technical devices into fully or partially operational and faulty. We give explicit expressions for the probabilities of fault detection in both parts of the system and for error probabilities of the first and second kind. We also show illustrative examples.