Instead of considering multi-component systems in a binary world, where systems and components are either up (operational, working) or down (nonoperational, failed), we move to a multi-variate one, where the system’s state space is partitioned into several performance levels, while components are as usual binary ones, subject to failures and possibly repairs. This allows defining performability metrics, where performance and dependability aspects are simultaneously taken into account. Consider an undirected graph whose nodes and/or edges can be failed or working, and where we are interested in the existence of paths composed only of working elements. Using a static (no time variable) setting, we consider the resilience metric that extends the classical connectivity-based ones such as the source-to-terminal reliability, or the all-terminal reliability. Resilience is defined as the expectation of the number of pairs of nodes that can communicate. After analyzing some basic examples, we briefly describe a Monte Carlo approach where instead of reducing the variance of the estimators, we focus on reducing their time complexities. This view allows a first straightforward way of exploring resilience (as well as many other classical metrics). It also allows easily performing a sensitivity analysis with respect to the individual reliabilities of the components, without a significant overhead of the procedure that estimates the resilience metric alone. The talk is based on the paper cited below.