Techniques for rare event analysis and applications

When systems are complex and critical, and when we are interested in their dependability properties (reliability, availability in its many forms, etc.), only simulation can be used for their analysis: if the system is complex, analytical and numerical procedures are in general useless. In this situation, the main difficulty relies in the rare event problem: if the system is critical, catastrophic failures have small probabilities to occur (but huge consequences, making their study critical as well). In this talk we briefly describe the two main families of Monte Carlo techniques that are used today in the area: Importance Sampling and the specific Zero-Variance approach, and Splitting procedures. Some examples will illustrate the presentation.