A probabilistic analysis of fault detection latency in a network of Finite State Machines

This paper suggests an approach to the computation of time probability distribution function (PDF) of Fault Detection Latency (FDL) in case, when a system is modeled as a combination of interacting finite state machines (FSMs) under randominputs, where the interactions deal with switching each of the FSMs froma working mode to a testing one. Fault detection latency is a period of fault detection after it occurs in certain inner states. Traditionally, the FDL of an FSM is modeled as the time (numbers of its state transition steps) to absorption for a Markov chain with the state space generated by a product of fault-free and faulty (i.e., corrupted by a fault) FSMs. The principal problem of using this model for the networks of sub-FSMs is that random transitions of the product of the fault-free and faulty networked automata even under independent inputs randomvectors are not theMarkovian ones. Thanks to an extension of the transition space of the networked FSMs by some additional states corresponding to the number of steps between transitions to the modes mentioned above for each of sub-FSMs, this model is extended to the case of an FSM decomposed (in a designing process) into a number of components of sub-FSMs. A way to compute the FDL PDF in terms of FDL PDF of initial FSM (that is not decomposed) and the FSMs of corresponding sub-FSMs is shown.