Probabilistic Calculations for Large Boolean Models

This chapter aims to explain how to overcome the shortcomings of the Sylvester-Poincaré formula by implementing calculation techniques based on the binary decision diagrams (BDDs). It explains, with simple examples, how the Shannon decomposition of the related logic formulae leads to build equivalent BDDs. Then, it explains how to do that directly from fault trees. It describes how the main problem of BDDs (i.e. the size which varies very much according to the ordering of the logic variables used to develop it) can be mitigated by using relevant heuristics. Then it illustrates the flexibility of BDDs for probabilistic calculations (probability of success or failure as well as conditional probabilities) and minimal cut and tie set identification and calculations. At the present time, the use of BDDs represents the state of the art with regards to calculations based on Boolean models.