  Repetitive Scenario Design (RSD) is a randomized approach to robust design
based on iterating two phases: a standard scenario design phase that uses $N$
scenarios (design samples), followed by randomized feasibility phase that uses
$N_o$ test samples on the scenario solution. We give a full and exact
probabilistic characterization of the number of iterations required by the RSD
approach for returning a solution, as a function of $N$, $N_o$, and of the
desired levels of probabilistic robustness in the solution. This novel approach
broadens the applicability of the scenario technology, since the user is now
presented with a clear tradeoff between the number $N$ of design samples and
the ensuing expected number of repetitions required by the RSD algorithm. The
plain (one-shot) scenario design becomes just one of the possibilities, sitting
at one extreme of the tradeoff curve, in which one insists in finding a
solution in a single repetition: this comes at the cost of possibly high $N$.
Other possibilities along the tradeoff curve use lower $N$ values, but possibly
require more than one repetition.
