  Weakly hard real-time systems can, to some degree, tolerate deadline misses,
but their schedulability still needs to be analyzed to ensure their quality of
service. Such analysis usually occurs at early design stages to provide
implementation guidelines to engineers so that they can make better design
decisions. Estimating worst-case execution times (WCET) is a key input to
schedulability analysis. However, early on during system design, estimating
WCET values is challenging and engineers usually determine them as plausible
ranges based on their domain knowledge. Our approach aims at finding
restricted, safe WCET sub-ranges given a set of ranges initially estimated by
experts in the context of weakly hard real-time systems. To this end, we
leverage (1) multi-objective search aiming at maximizing the violation of
weakly hard constraints in order to find worst-case scheduling scenarios and
(2) polynomial logistic regression to infer safe WCET ranges with a
probabilistic interpretation. We evaluated our approach by applying it to an
industrial system in the satellite domain and several realistic synthetic
systems. The results indicate that our approach significantly outperforms a
baseline relying on random search without learning, and estimates safe WCET
ranges with a high degree of confidence in practical time (< 23h).
