A new methodology to handle Boolean models with loops

It is often convenient, in reliability analyses, to describe the system under study by means of a set of Boolean equations. Fault trees can be seen as hierarchical sets of Boolean equations. In some cases, the model contains loops, because the system embeds at least two components whose states depend on one another. Reliability networks are a typical example of looped models. Classical fault tree assessment methods fail to assess this kind of model. This paper proposes a logical framework to clarify the meaning of looped sets of Boolean equations; and a binary decision diagrams based method is proposed to assess them. This approach is illustrated with experimental results on a benchmark of reliability networks.