We propose a new method to obtain bounds of dependability, performance or p
erformability measures concerning complex systems modeled by a large Markov
model. It extends previously published techniques mainly designed to the a
nalysis of dependability measures only and working under more restrictive c
onditions. Our approach allows us to obtain tight bounds of performance mea
sures on certain cases and, in particular, on models having an infinite sta
te space. We illustrate the method with some analytically intractable open
queuing networks, as well as with large dependability models.