ABSTRACT
Safety and risk analyses rely on models. These models have several important characteristics. They are event-oriented. The system under study changes of state when events, such as failure, hazard, repair and so on, occur. They are probabilistic. The exact moment of the occurrence of a failure is in essence unpredictable. They are discrete. States are represented by means of variables that take their values into finite, usually very small, domains. The most widely used modeling formalisms such as Fault Trees, Block Diagrams and Event Trees rely on Boolean algebra. There are cases however where binary states are not sufficient. For instance, it is sometimes necessary to represent the level of degradation of a component, the quality of a signal, and so on. This kind of models can be easily represented with AltaRica 3.0 – a high level modeling language dedicated to safety analyses. AltaRica 3.0 is at the core of the OpenAltaRica project which aim is to develop a complete set of assessment tools for the language, including among others compilers to Fault Trees and Markov Chains, stochastic and stepwise simulators. In this article we study how the notion of prime implicants can be extended to finite domain calculus. We discuss the efficient implementation of finite domain calculus and show how these results can be applied to simplify Fault Trees, automatically generated from AltaRica 3.0 models. This simplification in its turn significantly improves the efficiency of the assessment of the automatically generated Fault Trees.
