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