Reliability modeling of a hard real-time system using the path-space approach

A hard real-time system, such as a fly-by-wire system, fails catastrophically (e.g. losing stability) if its control inputs are not updated by its digital controller computer within a certain timing constraint called the hard deadline. To assess and validate those systems’ reliabilities 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 should recover quickly. Analytical bounds are derived for both exponential and Weibull failure distributions encountered commonly, 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.