A new formalism that combines advantages of fault-trees and Markov models: Boolean logic driven Markov processes

This paper introduces a modeling formalism that enables the analyst to combine concepts inherited from fault trees and Markov models in a new way. We call this formalism Boolean logic Driven Markov Processes (BDMP). It has two advantages over conventional models used in dependability assessment: it allows the definition of complex dynamic models while remaining nearly as readable and easy to build as fault-trees, and it offers interesting mathematical properties, which enable an efficient processing for BDMP that are equivalent to Markov processes with huge state spaces. We give a mathematical definition of BDMP, the demonstration of their properties, and several examples to illustrate how powerful and easy to use they are. From a mathematical point of view, a BDMP is nothing more than a certain way to define a global Markov process, as the result of several elementary processes which can interact in a given manner. An extreme case is when the processes are independent. Then we simply have a fault-tree, the leaves of which are associated to independent Markov processes.