Reliability modeling of real-time systems with deadline information

We consider the reliability of real-time systems that can handle temporary malfunctions of the controller-caused, for example, by electromagnetic interferences-without a total system failure. Unlike conventional reliability models that do not consider the timing constraints in recovering from a controller failure, our model embeds into a semi-Markov model the control system deadline (CSD) that depends on plant dynamics. We can therefore capture the interplay between the controller and the plant for safe operation by characterizing the system into three states: system-up, system-down/controller failure, and system failure. Based on this model, we compute the probability of a system failure by time T by taking the path-space approach to generate the formulas of the upper and the lower bounds, (instead of using the usual Chapman-Kolmogorov equations which are computationally intractable for our problem). Using three typical examples-assembly lines (large granule of time), aircraft control (short mission), and satellite control (long mission)-we show that the formulas are easy to use and give tight bounds for the highly-reliable systems of interest