Finite Degradation Structures.

Probabilistic risk and safety analyses are used in virtually all industries to assess whether the risk of operating complex technical systems is low enough to be socially acceptable. As of today, these analyses rely mainly on stochastic Boolean models such as fault trees or reliability block diagrams. These models are coarse approximations of the behavior of the systems under study. In this article, we introduce the notion of finite degradation structure. Finite degradation structures encode the degradation order among the states of multistate systems, i.e. models in which variables can take a finite number of values rather than just two. This extension of Boolean formalisms makes it possible to increase significantly the capacity of expression without increasing significantly the complexity of the calculation of risk indicators. Technically, finite degradation structures are finite semi-lattices associated with a random process. They form a monoidal category and provide a unified algebraic framework for Boolean reliability models and multistate systems. They shed a new light on central notions of system reliability theory such as those of coherent models and minimal cutsets.

Authors

• Antoine Rauzy
• Liu Yang

Keywords

• Multivalued logics
• category theory
• system reliability theory
• combinatorial models
• finite degradation structures