A hard real-time control system, such as a fly-by-wire system, fails catastrophically (e.g., lose stability) if its control input is not updated by its digital controller computer within a certain time limit called the hard deadline. To assess and validate system reliability by using a semi-Markov model that explicitly contains the deadline information, we propose a path-space approach deriving the upper and lower bounds of the probability of system failure. These bounds are derived by using only simple parameters, and they are especially suitable for highly-reliable systems which must recover quickly. Analytical bounds are derived for both exponential and Weibull failure distributions, which have proven effective through numerical examples, while considering three repair strategies: repair-as-good-as-new, repair-as-good-as-old, and repair-better-than-old.
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